diff --git a/src/.relint.yml b/src/.relint.yml
index 86684ad1040..617c086c109 100644
--- a/src/.relint.yml
+++ b/src/.relint.yml
@@ -49,6 +49,6 @@
     Hint: namespace package. Type import_statements("SOME_IDENTIFIER") to find a more specific import,
     Hint: or use 'sage --fiximports' to fix automatically in the source file.
   # Keep in sync with SAGE_ROOT/src/sage/misc/replace_dot_all.py
-  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings|sets))[.]all\s+import'
+  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings(|[.]finite_rings)|sets))[.]all\s+import'
   filePattern: '.*[.](py|pyx|pxi)$'
   error: false # Make this a warning instead of an error for now
diff --git a/src/sage/arith/multi_modular.pyx b/src/sage/arith/multi_modular.pyx
index 2958315c346..766c9923404 100644
--- a/src/sage/arith/multi_modular.pyx
+++ b/src/sage/arith/multi_modular.pyx
@@ -16,7 +16,7 @@ from cysignals.memory cimport check_allocarray, check_reallocarray, sig_free
 
 from sage.libs.gmp.mpz cimport *
 from sage.rings.integer cimport Integer, smallInteger
-from sage.arith.all import random_prime
+from sage.arith.misc import random_prime
 from types import GeneratorType
 from sage.ext.stdsage cimport PY_NEW
 from cpython.object cimport PyObject_RichCompare
diff --git a/src/sage/arith/numerical_approx.pyx b/src/sage/arith/numerical_approx.pyx
index b53d7679099..005b88621c4 100644
--- a/src/sage/arith/numerical_approx.pyx
+++ b/src/sage/arith/numerical_approx.pyx
@@ -15,7 +15,9 @@ Generic numerical approximation function
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport parent
 cdef Parent CDF
-from sage.rings.all import RealField, ComplexField, CDF
+from sage.rings.real_mpfr import RealField
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.complex_double import CDF
 
 
 def numerical_approx_generic(x, prec):
diff --git a/src/sage/crypto/boolean_function.pyx b/src/sage/crypto/boolean_function.pyx
index 13b8a1c82a1..adb2405457e 100644
--- a/src/sage/crypto/boolean_function.pyx
+++ b/src/sage/crypto/boolean_function.pyx
@@ -38,8 +38,7 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.polynomial.pbori.pbori import BooleanPolynomial
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.misc.superseded import deprecated_function_alias
@@ -329,11 +328,15 @@ cdef class BooleanFunction(SageObject):
 
         elif isinstance(x, Polynomial):
             K = x.base_ring()
-            if is_FiniteField(K) and K.characteristic() == 2:
+            if isinstance(K, FiniteField) and K.characteristic() == 2:
                 self._nvariables = K.degree()
                 bitset_init(self._truth_table, <mp_bitcnt_t> (1<<self._nvariables))
                 bitset_zero(self._truth_table)
-                if isinstance(K,FiniteField_givaro): #the ordering is not the same in this case
+                try:
+                    from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+                except ImportError:
+                    FiniteField_givaro = ()
+                if isinstance(K, FiniteField_givaro):  # the ordering is not the same in this case
                     for u in K:
                         bitset_set_to(self._truth_table, ZZ(u._vector_().list(),2) , (x(u)).trace())
                 else:
@@ -1008,7 +1011,7 @@ cdef class BooleanFunction(SageObject):
         from sage.misc.misc_c import prod
 
         from sage.matrix.constructor import Matrix
-        from sage.arith.all import binomial
+        from sage.arith.misc import binomial
         M = Matrix(GF(2), sum(binomial(self._nvariables,i) for i in range(d+1)), len(s))
 
         cdef long i
diff --git a/src/sage/crypto/classical.py b/src/sage/crypto/classical.py
index 39cab2a6f90..132a18cdee0 100644
--- a/src/sage/crypto/classical.py
+++ b/src/sage/crypto/classical.py
@@ -55,7 +55,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-from sage.arith.all import xgcd, inverse_mod
+from sage.arith.misc import inverse_mod, xgcd
 from random import randint
 from sage.matrix.matrix_space import MatrixSpace
 
diff --git a/src/sage/crypto/lattice.py b/src/sage/crypto/lattice.py
index cf72c2660c4..d7ee358b9a9 100644
--- a/src/sage/crypto/lattice.py
+++ b/src/sage/crypto/lattice.py
@@ -256,7 +256,7 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
             A = A.stack(R.random_element().matrix())
 
     elif type == 'cyclotomic':
-        from sage.arith.all import euler_phi
+        from sage.arith.misc import euler_phi
         from sage.misc.functional import cyclotomic_polynomial
 
         # we assume that n+1 <= min( euler_phi^{-1}(n) ) <= 2*n
diff --git a/src/sage/crypto/lfsr.py b/src/sage/crypto/lfsr.py
index 40b469652ec..b8aad014e27 100644
--- a/src/sage/crypto/lfsr.py
+++ b/src/sage/crypto/lfsr.py
@@ -128,8 +128,9 @@
 import copy
 
 from sage.structure.all import Sequence
-from sage.rings.all import Integer, PolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
+from sage.rings.integer import Integer
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 
 def lfsr_sequence(key, fill, n):
@@ -179,7 +180,7 @@ def lfsr_sequence(key, fill, n):
         raise TypeError("key must be a list")
     key = Sequence(key)
     F = key.universe()
-    if not is_FiniteField(F):
+    if not isinstance(F, FiniteField):
         raise TypeError("universe of sequence must be a finite field")
 
     s = fill
diff --git a/src/sage/crypto/lwe.py b/src/sage/crypto/lwe.py
index bc027e97362..815ecfa56ab 100644
--- a/src/sage/crypto/lwe.py
+++ b/src/sage/crypto/lwe.py
@@ -91,23 +91,25 @@
 - [CGW2013]_
 """
 
+from sage.arith.misc import euler_phi, next_prime
 from sage.functions.log import log
 from sage.functions.other import floor, ceil
-from sage.misc.functional import sqrt
 from sage.misc.functional import cyclotomic_polynomial, round
-from sage.misc.randstate import set_random_seed
+from sage.misc.functional import sqrt
 from sage.misc.prandom import randint
+from sage.misc.randstate import set_random_seed
 from sage.modules.free_module import FreeModule
 from sage.modules.free_module_element import random_vector, vector
 from sage.numerical.optimize import find_root
-from sage.rings.all import ZZ, IntegerModRing, RR
-from sage.arith.all import next_prime, euler_phi
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_mpfr import RR
+from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
+from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 from sage.structure.element import parent
 from sage.structure.sage_object import SageObject
 from sage.symbolic.constants import pi
 from sage.symbolic.ring import SR
-from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
-from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 
 
 class UniformSampler(SageObject):
diff --git a/src/sage/crypto/mq/rijndael_gf.py b/src/sage/crypto/mq/rijndael_gf.py
index fc3473d1b06..ec8f433d705 100644
--- a/src/sage/crypto/mq/rijndael_gf.py
+++ b/src/sage/crypto/mq/rijndael_gf.py
@@ -424,7 +424,8 @@
 
 from sage.matrix.constructor import matrix
 from sage.matrix.constructor import column_matrix
-from sage.structure.element import Matrix
+from sage.structure.element import Element, Matrix
+from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_base
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.structure.sage_object import SageObject
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -757,10 +758,9 @@ def _GF_to_hex(self, GF):
             sage: rgf._GF_to_hex(output)
             'e142cd5fcd9d6d94a3340793034391b5'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self._F))
@@ -883,10 +883,9 @@ def _GF_to_bin(self, GF):
             sage: rgf._GF_to_bin(output)
             '11011000000111111111100000011011110110000001111111111000000110111101100000011111111110000001101111011000000111111111100000011011'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self))
diff --git a/src/sage/crypto/public_key/blum_goldwasser.py b/src/sage/crypto/public_key/blum_goldwasser.py
index d841e69699a..8f076a4f70d 100644
--- a/src/sage/crypto/public_key/blum_goldwasser.py
+++ b/src/sage/crypto/public_key/blum_goldwasser.py
@@ -30,17 +30,16 @@
 
 from operator import xor
 
+from sage.arith.misc import gcd, power_mod, xgcd
 from sage.crypto.cryptosystem import PublicKeyCryptosystem
-from sage.crypto.util import is_blum_prime
-from sage.crypto.util import least_significant_bits
-from sage.crypto.util import random_blum_prime
+from sage.crypto.util import is_blum_prime, least_significant_bits, random_blum_prime
 from sage.functions.log import log
 from sage.functions.other import Function_floor
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import gcd, power_mod, xgcd
 from sage.rings.finite_rings.integer_mod import Mod as mod
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 
+
 floor = Function_floor()
 IntegerModRing = IntegerModFactory("IntegerModRing")
 
diff --git a/src/sage/crypto/sbox.pyx b/src/sage/crypto/sbox.pyx
index 5c63e79bbac..33c23bc8fb1 100644
--- a/src/sage/crypto/sbox.pyx
+++ b/src/sage/crypto/sbox.pyx
@@ -17,7 +17,7 @@ from sage.misc.functional import is_even
 from sage.misc.misc_c import prod as mul
 from sage.misc.superseded import deprecated_function_alias
 from sage.modules.free_module_element import vector
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.ideal import FieldIdeal, Ideal
 from sage.rings.integer_ring import ZZ
@@ -195,7 +195,7 @@ cdef class SBox(SageObject):
 
         _S_list = []
         for e in S:
-            if is_FiniteFieldElement(e):
+            if isinstance(e, Element) and isinstance(e.parent(), FiniteField):
                 e = e.polynomial().change_ring(ZZ).subs(e.parent().characteristic())
             _S_list.append(e)
         S = _S_list
diff --git a/src/sage/crypto/stream.py b/src/sage/crypto/stream.py
index 90e4a6f5133..8526aca4c44 100644
--- a/src/sage/crypto/stream.py
+++ b/src/sage/crypto/stream.py
@@ -12,12 +12,11 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .cryptosystem import SymmetricKeyCryptosystem
-from .stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
-
+from sage.arith.misc import gcd, power_mod
+from sage.crypto.cryptosystem import SymmetricKeyCryptosystem
+from sage.crypto.stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
 from sage.crypto.util import random_blum_prime
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import gcd, power_mod
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 from sage.rings.polynomial.polynomial_element import Polynomial
diff --git a/src/sage/crypto/util.py b/src/sage/crypto/util.py
index aa013f9aca4..637738e45d0 100644
--- a/src/sage/crypto/util.py
+++ b/src/sage/crypto/util.py
@@ -20,14 +20,16 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+from sage.arith.functions import lcm
+from sage.arith.misc import is_prime, primes, random_prime
+from sage.misc.lazy_import import lazy_import
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import is_prime, lcm, primes, random_prime
-from sage.rings.integer import Integer
 from sage.rings.finite_rings.integer_mod import Mod as mod
+from sage.rings.integer import Integer
 
-from sage.misc.lazy_import import lazy_import
 lazy_import('sage.arith.misc', ('carmichael_lambda'), deprecation=34719)
 
+
 def ascii_integer(B):
     r"""
     Return the ASCII integer corresponding to the binary string ``B``.
diff --git a/src/sage/databases/findstat.py b/src/sage/databases/findstat.py
index 452abbcce8e..0f3039d5a2c 100644
--- a/src/sage/databases/findstat.py
+++ b/src/sage/databases/findstat.py
@@ -1499,7 +1499,8 @@ def __call__(self, elt):
             from sage.repl.preparse import preparse
             try:
                 l = {}
-                code = "from sage.all import *\n" + preparse(self.sage_code())
+                environment = 'sage.all'
+                code = f"from {environment} import *\n" + preparse(self.sage_code())
                 exec(code, l)
             except SyntaxError:
                 raise ValueError("could not execute verified code for %s" % self)
diff --git a/src/sage/databases/jones.py b/src/sage/databases/jones.py
index 97741e98be5..6f6318d0c2d 100644
--- a/src/sage/databases/jones.py
+++ b/src/sage/databases/jones.py
@@ -68,7 +68,9 @@
 
 import os
 
-from sage.rings.all import NumberField, RationalField, PolynomialRing
+from sage.rings.number_field.number_field import NumberField
+from sage.rings.rational_field import RationalField
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.misc.misc import powerset
 from sage.env import SAGE_SHARE
 
diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
index ccf1de6115d..e672314a9c0 100644
--- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
@@ -43,8 +43,7 @@ class initialization directly.
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import typecall
 from sage.rings.integer import Integer
-from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
 from sage.rings.fraction_field import is_FractionField
 from sage.rings.quotient_ring import is_QuotientRing
@@ -251,7 +250,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
                 raise ValueError('domain and codomain do not agree')
             if R not in Fields():
                 return typecall(cls, polys, domain)
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 return DynamicalSystem_affine_finite_field(polys, domain)
             return DynamicalSystem_affine_field(polys, domain)
         elif isinstance(morphism_or_polys,(list, tuple)):
@@ -299,7 +298,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
 
         if R not in Fields():
             return typecall(cls, polys, domain)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return DynamicalSystem_affine_finite_field(polys, domain)
         return DynamicalSystem_affine_field(polys, domain)
 
@@ -319,7 +318,8 @@ def __init__(self, polys_or_rat_fncts, domain):
         """
         L = polys_or_rat_fncts
         # Next attribute needed for _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(L[0].base_ring())
+        R = L[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
         DynamicalSystem.__init__(self, L, domain)
 
     def __copy__(self):
diff --git a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
index b1e5240e90f..3688fb66623 100644
--- a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
+++ b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
@@ -22,22 +22,23 @@
 from copy import copy, deepcopy
 from itertools import permutations, combinations, product
 
+from sage.arith.functions import lcm
+from sage.arith.misc import CRT, divisors, gcd, is_square
+from sage.combinat.permutation import Arrangements
 from sage.combinat.subset import Subsets
-from sage.misc.functional import sqrt
 from sage.matrix.constructor import matrix
-from sage.structure.element import is_Matrix
+from sage.misc.functional import sqrt
 from sage.misc.misc_c import prod
+from sage.parallel.use_fork import p_iter_fork
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Integers
 from sage.rings.integer_ring import ZZ
 from sage.rings.number_field.number_field import NumberField
-from sage.arith.all import gcd, lcm, CRT, is_square, divisors
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 from sage.sets.primes import Primes
 from sage.sets.set import Set
-from sage.combinat.permutation import Arrangements
-from sage.parallel.use_fork import p_iter_fork
+from sage.structure.element import is_Matrix
 
 
 def automorphism_group_QQ_fixedpoints(rational_function, return_functions=False, iso_type=False):
diff --git a/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py b/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
index 65c6671ce59..735e0800a6f 100644
--- a/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
+++ b/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
@@ -34,7 +34,7 @@
 from sage.rings.rational_field import QQ
 from sage.schemes.affine.affine_space import AffineSpace
 from sage.symbolic.constants import e
-from sage.arith.all import gcd
+from sage.arith.misc import gcd
 from copy import copy
 
 def bCheck(c, v, p, b):
diff --git a/src/sage/dynamics/arithmetic_dynamics/generic_ds.py b/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
index 3e227942256..25d8645ae86 100644
--- a/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
@@ -33,7 +33,7 @@ class initialization directly.
 from sage.schemes.affine.affine_space import is_AffineSpace
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.qqbar import AlgebraicField_common
 from sage.schemes.berkovich.berkovich_space import is_Berkovich_Cp
 from sage.rings.rational_field import QQ
@@ -416,7 +416,7 @@ def field_of_definition_critical(self, return_embedding=False, simplify_all=Fals
             CR = CR.ring()
         x = CR.gen(0)
         poly = (g*CR(f).derivative(x) - f*CR(g).derivative(x)).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -536,7 +536,7 @@ def field_of_definition_periodic(self, n, formal=False, return_embedding=False,
             fn = ds.nth_iterate_map(n)
             f,g = fn[0].numerator(), fn[0].denominator()
             poly = (f - g*x).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -630,7 +630,7 @@ def field_of_definition_preimage(self, point, n, return_embedding=False, simplif
             #want the polynomial ring not the fraction field
             CR = CR.ring()
         poly = (f*point[1] - g*CR(point[0])).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index 385ccad1a91..4dd109036d4 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -52,32 +52,49 @@ class initialization directly.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.arith.misc import is_prime
+from copy import copy
+from itertools import count, product
+
+import sage.rings.abc
+
+from sage.arith.functions import lcm
+from sage.arith.misc import binomial, gcd, is_prime, moebius, next_prime, primes
 from sage.calculus.functions import jacobian
 from sage.categories.fields import Fields
+from sage.categories.finite_fields import FiniteFields
 from sage.categories.function_fields import FunctionFields
-from sage.categories.number_fields import NumberFields
 from sage.categories.homset import End
+from sage.categories.number_fields import NumberFields
+from sage.dynamics.arithmetic_dynamics.endPN_automorphism_group import (
+    automorphism_group_QQ_CRT,
+    automorphism_group_QQ_fixedpoints,
+    conjugating_set_helper,
+    conjugating_set_initializer,
+    is_conjugate_helper)
+from sage.dynamics.arithmetic_dynamics.endPN_automorphism_group import automorphism_group_FF
 from sage.dynamics.arithmetic_dynamics.generic_ds import DynamicalSystem
-from sage.misc.functional import sqrt
+from sage.dynamics.arithmetic_dynamics.projective_ds_helper import (
+    _fast_possible_periods,
+    _all_periodic_points)
 from sage.functions.other import ceil
 from sage.libs.pari.all import PariError
 from sage.matrix.constructor import matrix, identity_matrix
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import typecall
+from sage.misc.functional import sqrt
 from sage.misc.mrange import xmrange
 from sage.modules.free_module_element import vector
-from sage.rings.integer import Integer
-from sage.arith.all import gcd, lcm, next_prime, binomial, primes, moebius
-from sage.categories.finite_fields import FiniteFields
+from sage.parallel.ncpus import ncpus
+from sage.parallel.use_fork import p_iter_fork
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
 from sage.rings.complex_mpfr import ComplexField
-from sage.rings.finite_rings.finite_field_constructor import (is_FiniteField, GF,
-                                                              is_PrimeFiniteField)
+from sage.rings.finite_rings.finite_field_base import FiniteField
+from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Zmod
 from sage.rings.fraction_field import (FractionField, is_FractionField, FractionField_1poly_field)
 from sage.rings.fraction_field_element import is_FractionFieldElement, FractionFieldElement
 from sage.rings.function_field.function_field import is_FunctionField
+from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.flatten import FlatteningMorphism, UnflatteningMorphism
 from sage.rings.morphism import RingHomomorphism_im_gens
@@ -89,31 +106,17 @@ class initialization directly.
 from sage.rings.qqbar import QQbar, number_field_elements_from_algebraics
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.rational_field import QQ
-import sage.rings.abc
 from sage.rings.real_mpfr import RealField
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
-from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
+from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
 from sage.schemes.projective.projective_morphism import (
     SchemeMorphism_polynomial_projective_space,
     SchemeMorphism_polynomial_projective_space_field,
     SchemeMorphism_polynomial_projective_space_finite_field)
-from sage.schemes.projective.projective_space import (ProjectiveSpace,
-                                                      is_ProjectiveSpace)
-from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
+from sage.schemes.projective.projective_space import ProjectiveSpace, is_ProjectiveSpace
+from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
 from sage.structure.element import get_coercion_model
 from sage.symbolic.constants import e
-from copy import copy
-from sage.parallel.ncpus import ncpus
-from sage.parallel.use_fork import p_iter_fork
-from sage.dynamics.arithmetic_dynamics.projective_ds_helper import (_fast_possible_periods,_all_periodic_points)
-from itertools import count, product
-from .endPN_automorphism_group import (
-    automorphism_group_QQ_CRT,
-    automorphism_group_QQ_fixedpoints,
-    conjugating_set_helper,
-    conjugating_set_initializer,
-    is_conjugate_helper)
-from .endPN_automorphism_group import automorphism_group_FF
 
 
 class DynamicalSystem_projective(SchemeMorphism_polynomial_projective_space,
@@ -373,7 +376,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
                 raise ValueError('"domain" must be a projective scheme')
             if R not in Fields():
                 return typecall(cls, polys, domain)
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 return DynamicalSystem_projective_finite_field(polys, domain)
             return DynamicalSystem_projective_field(polys, domain)
 
@@ -432,7 +435,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
                 if not all(split_d == domain._degree(f) for f in split_poly):
                     msg = 'polys (={}) must be multi-homogeneous of the same degrees (by component)'
                     raise TypeError(msg.format(polys))
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 from sage.dynamics.arithmetic_dynamics.product_projective_ds import DynamicalSystem_product_projective_finite_field
                 return DynamicalSystem_product_projective_finite_field(polys, domain)
             return DynamicalSystem_product_projective(polys, domain)
@@ -450,7 +453,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             raise ValueError('"domain" must be a projective scheme')
         if R not in Fields():
             return typecall(cls, polys, domain)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
                 return DynamicalSystem_projective_finite_field(polys, domain)
         return DynamicalSystem_projective_field(polys, domain)
 
@@ -469,8 +472,9 @@ def __init__(self, polys, domain):
                     (3/5*x^2 : y^2)
         """
         # Next attribute needed for _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(polys[0].base_ring())
-        DynamicalSystem.__init__(self,polys,domain)
+        R = polys[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
+        DynamicalSystem.__init__(self, polys, domain)
 
     def __copy__(self):
         r"""
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
index 0228711e7f3..40574bf6ea6 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
@@ -21,7 +21,7 @@ AUTHORS:
 
 from sage.arith.functions cimport LCM_list
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.sets.all import Set
+from sage.sets.set import Set
 from sage.misc.misc import subsets
 
 cpdef _fast_possible_periods(self, return_points=False):
diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
index 1189b55fec9..1514c5bf5a8 100644
--- a/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
+++ b/src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx
@@ -38,7 +38,7 @@ from sage.symbolic.ring import SR
 from sage.calculus.var import var
 from sage.rings.fraction_field import is_FractionField
 from sage.categories.function_fields import FunctionFields
-from sage.libs.all import PariError
+from cypari2.handle_error import PariError
 from math import sqrt
 
 
@@ -944,7 +944,7 @@ cpdef general_julia(f, double x_center=0, double y_center=0, image_width=4,
     sage: from sage.dynamics.complex_dynamics.mandel_julia_helper import general_julia
     sage: from sage.plot.colors import Color
     sage: R.<z> = CC[]
-    sage: f = z^5 - 1 
+    sage: f = z^5 - 1
     sage: general_julia(f)
     500x500px 24-bit RGB image
     """
diff --git a/src/sage/groups/cubic_braid.py b/src/sage/groups/cubic_braid.py
index a9465ef2b3d..206eedb1856 100644
--- a/src/sage/groups/cubic_braid.py
+++ b/src/sage/groups/cubic_braid.py
@@ -1543,10 +1543,10 @@ def as_matrix_group(self, root_bur=None, domain=None, characteristic=None, var='
                 self._classical_invariant_form = herm_form
 
         if unitary:
-            from sage.rings.finite_rings.finite_field_base import is_FiniteField
+            from sage.rings.finite_rings.finite_field_base import FiniteField
             from sage.groups.matrix_gps.unitary import GU
             d, d = herm_form.dimensions()
-            if is_FiniteField(domain):
+            if isinstance(domain, FiniteField):
                 base_group = GU(d, domain, var=domain.gen(), invariant_form=herm_form)
             else:
                 base_group = GU(d, domain, invariant_form=herm_form)
diff --git a/src/sage/groups/matrix_gps/orthogonal.py b/src/sage/groups/matrix_gps/orthogonal.py
index 8ff96051a8b..242c3f42529 100644
--- a/src/sage/groups/matrix_gps/orthogonal.py
+++ b/src/sage/groups/matrix_gps/orthogonal.py
@@ -85,7 +85,7 @@
 # ****************************************************************************
 
 from sage.rings.integer_ring import ZZ
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
 from sage.groups.matrix_gps.named_group import (
@@ -127,7 +127,7 @@ def normalize_args_e(degree, ring, e):
         ...
         ValueError: must have e=-1 or e=1 for even degree
     """
-    if is_FiniteField(ring) and degree%2 == 0:
+    if isinstance(ring, FiniteField) and degree%2 == 0:
         if e not in (-1, +1):
             raise ValueError('must have e=-1 or e=1 for even degree')
     else:
@@ -171,7 +171,7 @@ def _OG(n, R, special, e=0, var='a', invariant_form=None):
     e = normalize_args_e(degree, ring, e)
 
     if invariant_form is not None:
-        if is_FiniteField(ring):
+        if isinstance(ring, FiniteField):
             raise NotImplementedError("invariant_form for finite groups is fixed by GAP")
 
     if e == 0:
@@ -202,7 +202,7 @@ def _OG(n, R, special, e=0, var='a', invariant_form=None):
                                                          latex(ring),
                                                          '+' if e == 1 else '-')
 
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         cmd  = '{0}O({1}, {2}, {3})'.format(ltx_prefix, e, degree, ring.order())
         return OrthogonalMatrixGroup_gap(degree, ring, False, name, ltx, cmd)
     else:
diff --git a/src/sage/groups/matrix_gps/symplectic.py b/src/sage/groups/matrix_gps/symplectic.py
index 3715f531913..8dd041af286 100644
--- a/src/sage/groups/matrix_gps/symplectic.py
+++ b/src/sage/groups/matrix_gps/symplectic.py
@@ -42,7 +42,7 @@
 
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.groups.matrix_gps.named_group import (
     normalize_args_vectorspace, normalize_args_invariant_form,
     NamedMatrixGroup_generic, NamedMatrixGroup_gap)
@@ -145,7 +145,7 @@ def Sp(n, R, var='a', invariant_form=None):
         raise ValueError('the degree must be even')
 
     if invariant_form is not None:
-        if is_FiniteField(ring):
+        if isinstance(ring, FiniteField):
             raise NotImplementedError("invariant_form for finite groups is fixed by GAP")
 
         invariant_form = normalize_args_invariant_form(ring, degree, invariant_form)
diff --git a/src/sage/groups/matrix_gps/unitary.py b/src/sage/groups/matrix_gps/unitary.py
index f4d8df525be..d8919f82695 100644
--- a/src/sage/groups/matrix_gps/unitary.py
+++ b/src/sage/groups/matrix_gps/unitary.py
@@ -50,7 +50,7 @@
 # ****************************************************************************
 
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
 from sage.groups.matrix_gps.named_group import (
@@ -77,7 +77,7 @@ def finite_field_sqrt(ring):
         sage: finite_field_sqrt(GF(4, 'a'))
         2
     """
-    if not is_FiniteField(ring):
+    if not isinstance(ring, FiniteField):
         raise ValueError('not a finite field')
     q, rem = ring.cardinality().sqrtrem()
     if rem:
@@ -107,7 +107,7 @@ def _UG(n, R, special, var='a', invariant_form=None):
         latex_prefix ='S'
 
     degree, ring = normalize_args_vectorspace(n, R, var=var)
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         q = ring.cardinality()
         ring = GF(q**2, name=var)
         if invariant_form is not None:
@@ -134,7 +134,7 @@ def _UG(n, R, special, var='a', invariant_form=None):
         name = '{0} Unitary Group of degree {1} over {2}'.format(prefix, degree, ring)
         ltx  = r'\text{{{0}U}}_{{{1}}}({2})'.format(latex_prefix, degree, latex(ring))
 
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         cmd = '{0}U({1}, {2})'.format(latex_prefix, degree, q)
         return UnitaryMatrixGroup_gap(degree, ring, special, name, ltx, cmd)
     else:
diff --git a/src/sage/interfaces/gap.py b/src/sage/interfaces/gap.py
index a38d2bd6d02..a87decbabbb 100644
--- a/src/sage/interfaces/gap.py
+++ b/src/sage/interfaces/gap.py
@@ -1753,7 +1753,7 @@ def intmod_gap_to_sage(x):
         sage: b.parent()
         Ring of integers modulo 65537
     """
-    from sage.rings.finite_rings.all import FiniteField
+    from sage.rings.finite_rings.finite_field_constructor import FiniteField
     from sage.rings.finite_rings.integer_mod import Mod
     from sage.rings.integer import Integer
     s = str(x)
diff --git a/src/sage/lfunctions/dokchitser.py b/src/sage/lfunctions/dokchitser.py
index c526b9321a4..58499396d6c 100644
--- a/src/sage/lfunctions/dokchitser.py
+++ b/src/sage/lfunctions/dokchitser.py
@@ -33,7 +33,7 @@
 import string
 
 from sage.structure.sage_object import SageObject
-from sage.rings.all import ComplexField
+from sage.rings.complex_mpfr import ComplexField
 from sage.rings.integer import Integer
 from sage.misc.sage_eval import sage_eval
 from sage.misc.verbose import verbose
diff --git a/src/sage/lfunctions/pari.py b/src/sage/lfunctions/pari.py
index f75b232e595..bbf289aa21c 100644
--- a/src/sage/lfunctions/pari.py
+++ b/src/sage/lfunctions/pari.py
@@ -22,7 +22,10 @@
 from cypari2.gen import Gen
 from sage.libs.pari import pari
 from sage.structure.sage_object import SageObject
-from sage.rings.all import (ZZ, RealField, ComplexField, PowerSeriesRing)
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_mpfr import RealField
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.power_series_ring import PowerSeriesRing
 
 
 class lfun_generic():
diff --git a/src/sage/lfunctions/zero_sums.pyx b/src/sage/lfunctions/zero_sums.pyx
index 2b0ca332b2a..1b584caec25 100644
--- a/src/sage/lfunctions/zero_sums.pyx
+++ b/src/sage/lfunctions/zero_sums.pyx
@@ -18,20 +18,21 @@ AUTHORS:
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sage_object cimport SageObject
-from sage.rings.integer_ring import ZZ
-from sage.rings.real_double import RDF
-from sage.rings.complex_double import CDF
-from sage.rings.infinity import PlusInfinity
-from sage.arith.all import prime_powers, next_prime
+from sage.arith.misc import next_prime, prime_powers
 from sage.functions.log import log, exp
 from sage.functions.other import real, imag
-from sage.symbolic.constants import pi, euler_gamma
+from sage.libs.flint.ulong_extras cimport n_is_prime
 from sage.libs.pari.all import pari
 from sage.misc.verbose import verbose
 from sage.parallel.decorate import parallel
 from sage.parallel.ncpus import ncpus as num_cpus
-from sage.libs.flint.ulong_extras cimport n_is_prime
+from sage.rings.complex_double import CDF
+from sage.rings.infinity import PlusInfinity
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_double import RDF
+from sage.structure.sage_object cimport SageObject
+from sage.symbolic.constants import euler_gamma, pi
+
 
 cdef extern from "<math.h>":
     double c_exp "exp"(double)
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index afd06c9db20..3a48b7bccbe 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -43,7 +43,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 import sage.rings.integer as integer
-import sage.rings.finite_rings.finite_field_constructor
+from sage.rings.finite_rings.finite_field_base import FiniteField
 import sage.misc.latex as latex
 import sage.modules.free_module
 
@@ -223,7 +223,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
                     else:
                         return matrix_complex_double_dense.Matrix_complex_double_dense
 
-            elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(R):
+            elif isinstance(R, FiniteField):
                 if R.order() == 2:
                     try:
                         from . import matrix_mod2_dense
diff --git a/src/sage/modules/free_module.py b/src/sage/modules/free_module.py
index 743fc2fbbcc..41bd5633503 100644
--- a/src/sage/modules/free_module.py
+++ b/src/sage/modules/free_module.py
@@ -183,7 +183,6 @@
 import sage.misc.latex as latex
 
 from sage.modules.module import Module
-import sage.rings.finite_rings.finite_field_constructor as finite_field
 import sage.rings.ring as ring
 import sage.rings.abc
 import sage.rings.integer_ring
@@ -195,6 +194,7 @@
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.randstate import current_randstate
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.structure.factory import UniqueFactory
 from sage.structure.sequence import Sequence
 from sage.structure.richcmp import (richcmp_method, rich_to_bool, richcmp,
@@ -6348,7 +6348,7 @@ def _element_constructor_(self, e, *args, **kwds):
         """
         try:
             k = e.parent()
-            if finite_field.is_FiniteField(k) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
+            if isinstance(k, FiniteField) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
                 return self(e._vector_())
         except AttributeError:
             pass
diff --git a/src/sage/quadratic_forms/binary_qf.py b/src/sage/quadratic_forms/binary_qf.py
index 6eebe6f0c46..4b85ad40ed7 100755
--- a/src/sage/quadratic_forms/binary_qf.py
+++ b/src/sage/quadratic_forms/binary_qf.py
@@ -52,8 +52,9 @@
 from functools import total_ordering
 
 from sage.libs.pari.all import pari_gen
-from sage.rings.all import ZZ, is_fundamental_discriminant
-from sage.arith.all import gcd
+from sage.rings.integer_ring import ZZ
+from sage.rings.number_field.number_field import is_fundamental_discriminant
+from sage.arith.misc import gcd
 from sage.structure.sage_object import SageObject
 from sage.matrix.matrix_space import MatrixSpace
 from sage.matrix.constructor import Matrix
@@ -1528,7 +1529,7 @@ def small_prime_value(self, Bmax=1000):
             sage: [Q.small_prime_value() for Q in BinaryQF_reduced_representatives(-47, primitive_only=True)]
             [47, 2, 2, 3, 3]
         """
-        from sage.sets.all import Set
+        from sage.sets.set import Set
         from sage.arith.srange import xsrange
         B = 10
         while True:
diff --git a/src/sage/quadratic_forms/count_local_2.pyx b/src/sage/quadratic_forms/count_local_2.pyx
index 36b6b9d593c..299554de655 100644
--- a/src/sage/quadratic_forms/count_local_2.pyx
+++ b/src/sage/quadratic_forms/count_local_2.pyx
@@ -2,13 +2,11 @@ r"""
 Optimized counting of congruence solutions
 """
 
-from sage.arith.all import valuation, kronecker_symbol, is_prime
+from sage.arith.misc import is_prime, kronecker as kronecker_symbol, valuation
+from sage.rings.finite_rings.integer_mod cimport IntegerMod_gmp
 from sage.rings.finite_rings.integer_mod import Mod
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-
 from sage.rings.integer_ring import ZZ
-
-from sage.rings.finite_rings.integer_mod cimport IntegerMod_gmp
 from sage.sets.set import Set
 
 
diff --git a/src/sage/quadratic_forms/extras.py b/src/sage/quadratic_forms/extras.py
index be7f05b0439..e042d3c037f 100644
--- a/src/sage/quadratic_forms/extras.py
+++ b/src/sage/quadratic_forms/extras.py
@@ -4,7 +4,7 @@
 
 from sage.matrix.constructor import matrix
 from sage.structure.element import is_Matrix
-from sage.arith.all import legendre_symbol
+from sage.arith.misc import legendre_symbol
 from sage.rings.integer_ring import ZZ
 
 
diff --git a/src/sage/quadratic_forms/genera/genus.py b/src/sage/quadratic_forms/genera/genus.py
index 5451df7ae29..51d4b82d339 100644
--- a/src/sage/quadratic_forms/genera/genus.py
+++ b/src/sage/quadratic_forms/genera/genus.py
@@ -22,7 +22,8 @@
 from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.misc.cachefunc import cached_method
-from sage.arith.all import LCM, fundamental_discriminant
+from sage.arith.functions import lcm as LCM
+from sage.arith.misc import fundamental_discriminant
 from sage.matrix.matrix_space import MatrixSpace
 from sage.matrix.constructor import matrix
 from sage.rings.integer_ring import IntegerRing, ZZ
diff --git a/src/sage/quadratic_forms/genera/normal_form.py b/src/sage/quadratic_forms/genera/normal_form.py
index bebd2478ec4..616cc5c516b 100644
--- a/src/sage/quadratic_forms/genera/normal_form.py
+++ b/src/sage/quadratic_forms/genera/normal_form.py
@@ -87,7 +87,9 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.rings.all import Zp, ZZ, GF
+from sage.rings.padics.factory import Zp
+from sage.rings.integer_ring import ZZ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.matrix.constructor import Matrix
 from copy import copy
 from sage.rings.finite_rings.integer_mod import mod
diff --git a/src/sage/quadratic_forms/genera/spinor_genus.py b/src/sage/quadratic_forms/genera/spinor_genus.py
index e42e4b6e361..8e77961b864 100644
--- a/src/sage/quadratic_forms/genera/spinor_genus.py
+++ b/src/sage/quadratic_forms/genera/spinor_genus.py
@@ -27,7 +27,8 @@
 
 from sage.groups.abelian_gps.abelian_group_gap import (AbelianGroupGap,
                                                        AbelianGroupElement_gap)
-from sage.rings.all import ZZ, QQ
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 
 
 class SpinorOperator(AbelianGroupElement_gap):
diff --git a/src/sage/quadratic_forms/qfsolve.py b/src/sage/quadratic_forms/qfsolve.py
index d5e15d9f83e..82b22328818 100644
--- a/src/sage/quadratic_forms/qfsolve.py
+++ b/src/sage/quadratic_forms/qfsolve.py
@@ -26,7 +26,9 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.rings.all import ZZ, QQ, Integer
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.integer import Integer
 from sage.modules.free_module_element import vector
 from sage.matrix.constructor import Matrix
 
diff --git a/src/sage/quadratic_forms/quadratic_form.py b/src/sage/quadratic_forms/quadratic_form.py
index 47f3d8be23e..4541759d86c 100644
--- a/src/sage/quadratic_forms/quadratic_form.py
+++ b/src/sage/quadratic_forms/quadratic_form.py
@@ -27,8 +27,10 @@
 from sage.rings.integer_ring import IntegerRing, ZZ
 from sage.rings.ring import Ring
 from sage.misc.functional import denominator, is_even
-from sage.arith.all import GCD, LCM
-from sage.rings.all import Ideal, QQ
+from sage.arith.misc import GCD
+from sage.arith.functions import lcm as LCM
+from sage.rings.ideal import Ideal
+from sage.rings.rational_field import QQ
 from sage.rings.ring import is_Ring, PrincipalIdealDomain
 from sage.structure.element import is_Vector
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
diff --git a/src/sage/quadratic_forms/quadratic_form__automorphisms.py b/src/sage/quadratic_forms/quadratic_form__automorphisms.py
index 3d72cf3be11..48a473f44c4 100644
--- a/src/sage/quadratic_forms/quadratic_form__automorphisms.py
+++ b/src/sage/quadratic_forms/quadratic_form__automorphisms.py
@@ -14,7 +14,7 @@
 
 from sage.modules.all import FreeModule
 from sage.modules.free_module_element import vector
-from sage.arith.all import GCD
+from sage.arith.misc import GCD
 
 
 @cached_method
diff --git a/src/sage/quadratic_forms/quadratic_form__equivalence_testing.py b/src/sage/quadratic_forms/quadratic_form__equivalence_testing.py
index b69bb6abf9d..3175126556d 100644
--- a/src/sage/quadratic_forms/quadratic_form__equivalence_testing.py
+++ b/src/sage/quadratic_forms/quadratic_form__equivalence_testing.py
@@ -5,11 +5,16 @@
 
 - Anna Haensch (2014-12-01): added test for rational isometry
 """
-from sage.arith.all import hilbert_symbol, prime_divisors, is_prime, valuation, GCD, legendre_symbol
-from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
 
+from sage.arith.misc import (hilbert_symbol,
+                             GCD,
+                             is_prime,
+                             legendre_symbol,
+                             prime_divisors,
+                             valuation)
 from sage.quadratic_forms.quadratic_form import is_QuadraticForm
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 
 
 ##############################################################################
diff --git a/src/sage/quadratic_forms/quadratic_form__genus.py b/src/sage/quadratic_forms/quadratic_form__genus.py
index 18a02061029..30bd73145f9 100644
--- a/src/sage/quadratic_forms/quadratic_form__genus.py
+++ b/src/sage/quadratic_forms/quadratic_form__genus.py
@@ -7,9 +7,9 @@
 #                                                           #
 #############################################################
 
+from sage.arith.misc import is_prime, prime_divisors
 from sage.quadratic_forms.genera.genus import Genus, LocalGenusSymbol
 from sage.rings.integer_ring import ZZ
-from sage.arith.all import is_prime, prime_divisors
 
 
 def global_genus_symbol(self):
diff --git a/src/sage/quadratic_forms/quadratic_form__local_density_congruence.py b/src/sage/quadratic_forms/quadratic_form__local_density_congruence.py
index 71872a37b8e..bf09113ae73 100644
--- a/src/sage/quadratic_forms/quadratic_form__local_density_congruence.py
+++ b/src/sage/quadratic_forms/quadratic_form__local_density_congruence.py
@@ -10,7 +10,7 @@
 
 from sage.sets.set import Set
 from sage.rings.rational_field import QQ
-from sage.arith.all import valuation
+from sage.arith.misc import valuation
 from sage.misc.verbose import verbose
 
 from sage.quadratic_forms.count_local_2 import count_modp__by_gauss_sum
diff --git a/src/sage/quadratic_forms/quadratic_form__local_density_interfaces.py b/src/sage/quadratic_forms/quadratic_form__local_density_interfaces.py
index aa4fb04ad63..2b8c1a455a4 100644
--- a/src/sage/quadratic_forms/quadratic_form__local_density_interfaces.py
+++ b/src/sage/quadratic_forms/quadratic_form__local_density_interfaces.py
@@ -4,7 +4,7 @@
 # // This is needed in the filter for primitivity...
 # #include "../max-min.h"
 
-from sage.arith.all import valuation
+from sage.arith.misc import valuation
 from sage.rings.rational_field import QQ
 
 
diff --git a/src/sage/quadratic_forms/quadratic_form__local_field_invariants.py b/src/sage/quadratic_forms/quadratic_form__local_field_invariants.py
index 3556c101705..cf0589872a6 100644
--- a/src/sage/quadratic_forms/quadratic_form__local_field_invariants.py
+++ b/src/sage/quadratic_forms/quadratic_form__local_field_invariants.py
@@ -21,15 +21,15 @@
 # places, is_semi_definite, and support for number fields.
 ###########################################################################
 
-
 from copy import deepcopy
-from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
-from sage.rings.real_mpfr import RR
-from sage.arith.all import prime_divisors, hilbert_symbol
+
+from sage.arith.misc import hilbert_symbol, prime_divisors
 from sage.functions.all import sgn
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.real_mpfr import RR
 
 
 def rational_diagonal_form(self, return_matrix=False):
diff --git a/src/sage/quadratic_forms/quadratic_form__local_normal_form.py b/src/sage/quadratic_forms/quadratic_form__local_normal_form.py
index 429c7c68896..2eb5839306d 100644
--- a/src/sage/quadratic_forms/quadratic_form__local_normal_form.py
+++ b/src/sage/quadratic_forms/quadratic_form__local_normal_form.py
@@ -21,7 +21,9 @@
 from sage.rings.infinity import Infinity
 from sage.rings.integer_ring import IntegerRing, ZZ
 from sage.rings.rational_field import QQ
-from sage.arith.all import GCD, valuation, is_prime
+from sage.arith.misc import GCD
+from sage.arith.misc import valuation
+from sage.arith.misc import is_prime
 
 
 def find_entry_with_minimal_scale_at_prime(self, p):
diff --git a/src/sage/quadratic_forms/quadratic_form__local_representation_conditions.py b/src/sage/quadratic_forms/quadratic_form__local_representation_conditions.py
index 5d39650ecb4..661078d8788 100644
--- a/src/sage/quadratic_forms/quadratic_form__local_representation_conditions.py
+++ b/src/sage/quadratic_forms/quadratic_form__local_representation_conditions.py
@@ -8,7 +8,7 @@
 from __future__ import annotations
 from copy import deepcopy
 
-from sage.arith.all import prime_divisors, valuation, is_square
+from sage.arith.misc import is_square, prime_divisors, valuation
 from sage.misc.functional import numerator, denominator
 from sage.quadratic_forms.extras import least_quadratic_nonresidue
 from sage.rings.infinity import infinity
diff --git a/src/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py b/src/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py
index 65c524db39a..551354251ce 100644
--- a/src/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py
+++ b/src/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py
@@ -1,12 +1,16 @@
 """
 Conway-Sloane masses
 """
+from sage.arith.misc import (fundamental_discriminant,
+                             is_prime,
+                             kronecker as kronecker_symbol,
+                             legendre_symbol,
+                             prime_divisors)
+from sage.misc.misc_c import prod
+from sage.quadratic_forms.special_values import gamma__exact, zeta__exact, quadratic_L_function__exact
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.arith.all import kronecker_symbol, legendre_symbol, prime_divisors, is_prime, fundamental_discriminant
 from sage.symbolic.constants import pi
-from sage.misc.misc_c import prod
-from sage.quadratic_forms.special_values import gamma__exact, zeta__exact, quadratic_L_function__exact
 
 
 def parity(self, allow_rescaling_flag=True):
diff --git a/src/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py b/src/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py
index 97b07023060..08b388d4285 100644
--- a/src/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py
+++ b/src/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py
@@ -12,17 +12,17 @@
 
 import copy
 
+from sage.arith.misc import kronecker, legendre_symbol, prime_divisors
+from sage.functions.all import sgn
+from sage.matrix.matrix_space import MatrixSpace
+from sage.misc.functional import squarefree_part
 from sage.misc.misc_c import prod
 from sage.misc.mrange import mrange
-from sage.rings.integer_ring import ZZ
+from sage.quadratic_forms.special_values import gamma__exact, zeta__exact, quadratic_L_function__exact
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.arith.all import legendre_symbol, kronecker, prime_divisors
-from sage.functions.all import sgn
-from sage.quadratic_forms.special_values import gamma__exact, zeta__exact, quadratic_L_function__exact
-from sage.misc.functional import squarefree_part
 from sage.symbolic.constants import pi
-from sage.matrix.matrix_space import MatrixSpace
 
 
 def mass__by_Siegel_densities(self, odd_algorithm="Pall", even_algorithm="Watson"):
diff --git a/src/sage/quadratic_forms/quadratic_form__neighbors.py b/src/sage/quadratic_forms/quadratic_form__neighbors.py
index 96a5203101d..11065d861aa 100644
--- a/src/sage/quadratic_forms/quadratic_form__neighbors.py
+++ b/src/sage/quadratic_forms/quadratic_form__neighbors.py
@@ -4,7 +4,8 @@
 
 from sage.modules.free_module_element import vector
 from sage.rings.integer_ring import ZZ
-from sage.rings.all import GF, QQ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
+from sage.rings.rational_field import QQ
 from copy import deepcopy
 from sage.matrix.constructor import matrix
 
diff --git a/src/sage/quadratic_forms/quadratic_form__siegel_product.py b/src/sage/quadratic_forms/quadratic_form__siegel_product.py
index 1cf72a23745..6c5118309c9 100644
--- a/src/sage/quadratic_forms/quadratic_form__siegel_product.py
+++ b/src/sage/quadratic_forms/quadratic_form__siegel_product.py
@@ -10,15 +10,15 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
-from sage.arith.all import kronecker_symbol, bernoulli, prime_divisors, fundamental_discriminant
+from sage.arith.misc import (bernoulli,
+                             fundamental_discriminant,
+                             kronecker as kronecker_symbol,
+                             prime_divisors)
 from sage.misc.functional import sqrt
-from sage.quadratic_forms.special_values import QuadraticBernoulliNumber
-
-
 from sage.misc.verbose import verbose
-
+from sage.quadratic_forms.special_values import QuadraticBernoulliNumber
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 
 
 #/*!  \brief Computes the product of all local densities for comparison with independently computed Eisenstein coefficients.
diff --git a/src/sage/quadratic_forms/quadratic_form__split_local_covering.py b/src/sage/quadratic_forms/quadratic_form__split_local_covering.py
index 2fc02f60e56..4078e6fede8 100644
--- a/src/sage/quadratic_forms/quadratic_form__split_local_covering.py
+++ b/src/sage/quadratic_forms/quadratic_form__split_local_covering.py
@@ -18,7 +18,7 @@
 from sage.matrix.constructor import matrix
 from sage.functions.all import floor
 from sage.rings.integer_ring import ZZ
-from sage.arith.all import GCD
+from sage.arith.misc import GCD
 
 
 def cholesky_decomposition(self, bit_prec = 53):
diff --git a/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py b/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py
index 22334a8e857..ff1476c32d9 100644
--- a/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py
+++ b/src/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py
@@ -11,17 +11,19 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.rings.integer_ring import ZZ
-from sage.misc.functional import is_odd
-
+from sage.arith.misc import (CRT_vectors,
+                             factor,
+                             gcd,
+                             hilbert_symbol,
+                             kronecker as kronecker_symbol,
+                             prime_to_m_part)
 from sage.libs.pari.all import pari
+from sage.misc.functional import is_odd
 from sage.misc.misc_c import prod
-from sage.arith.all import (factor, gcd, prime_to_m_part, CRT_vectors,
-        hilbert_symbol, kronecker_symbol)
-
-from sage.quadratic_forms.quadratic_form import QuadraticForm__constructor as QuadraticForm
 from sage.modules.free_module import FreeModule
 from sage.modules.free_module_element import vector
+from sage.quadratic_forms.quadratic_form import QuadraticForm__constructor as QuadraticForm
+from sage.rings.integer_ring import ZZ
 
 
 # TO DO -- Add second argument
diff --git a/src/sage/quadratic_forms/special_values.py b/src/sage/quadratic_forms/special_values.py
index af80989032e..dbfad45e31e 100644
--- a/src/sage/quadratic_forms/special_values.py
+++ b/src/sage/quadratic_forms/special_values.py
@@ -7,16 +7,21 @@
 - :func:`quadratic_L_function__numerical` -- Numerical values of the Dirichlet L-functions of quadratic characters in the domain of convergence
 """
 
+import sage.rings.abc
+
+from sage.arith.misc import (bernoulli,
+                             factorial,
+                             fundamental_discriminant,
+                             kronecker as kronecker_symbol)
 from sage.combinat.combinat import bernoulli_polynomial
 from sage.misc.functional import denominator
-from sage.arith.all import kronecker_symbol, bernoulli, factorial, fundamental_discriminant
 from sage.rings.infinity import infinity
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
-import sage.rings.abc
 from sage.symbolic.constants import pi, I
 
+
 # ---------------- The Gamma Function  ------------------
 
 def gamma__exact(n):
@@ -60,7 +65,7 @@ def gamma__exact(n):
         ...
         TypeError: you must give an integer or half-integer argument
     """
-    from sage.all import sqrt
+    from sage.misc.functional import sqrt
     n = QQ(n)
 
     if denominator(n) == 1:
@@ -213,7 +218,8 @@ def quadratic_L_function__exact(n, d):
     - [IR1990]_
     - [Was1997]_
     """
-    from sage.all import SR, sqrt
+    from sage.symbolic.ring import SR
+    from sage.misc.functional import sqrt
     if n <= 0:
         return QuadraticBernoulliNumber(1-n,d)/(n-1)
     elif n >= 1:
diff --git a/src/sage/quadratic_forms/ternary.pyx b/src/sage/quadratic_forms/ternary.pyx
index 168ef3392bb..727b31ce080 100644
--- a/src/sage/quadratic_forms/ternary.pyx
+++ b/src/sage/quadratic_forms/ternary.pyx
@@ -12,13 +12,13 @@ Helper code for ternary quadratic forms
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.rings.integer_ring import ZZ
+from sage.arith.misc import gcd, inverse_mod, xgcd
 from sage.matrix.constructor import matrix, identity_matrix, diagonal_matrix
+from sage.misc.prandom import randint
 from sage.modules.free_module_element import vector
-from sage.arith.all import inverse_mod, xgcd, gcd
 from sage.quadratic_forms.extras import extend_to_primitive
 from sage.rings.finite_rings.integer_mod import mod
-from sage.misc.prandom import randint
+from sage.rings.integer_ring import ZZ
 
 
 def red_mfact(a,b):
diff --git a/src/sage/quadratic_forms/ternary_qf.py b/src/sage/quadratic_forms/ternary_qf.py
index 7932c432779..bb98b11cb30 100644
--- a/src/sage/quadratic_forms/ternary_qf.py
+++ b/src/sage/quadratic_forms/ternary_qf.py
@@ -26,19 +26,25 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sage_object import SageObject
-from sage.rings.integer_ring import ZZ
-from sage.arith.all import gcd, kronecker_symbol
-from sage.quadratic_forms.quadratic_form import QuadraticForm
+from sage.arith.misc import gcd, kronecker as kronecker_symbol
 from sage.matrix.constructor import matrix, identity_matrix
-from sage.structure.element import is_Vector, is_Matrix
-from sage.quadratic_forms.ternary import _reduced_ternary_form_eisenstein_with_matrix
-from sage.quadratic_forms.ternary import _reduced_ternary_form_eisenstein_without_matrix, _find_zeros_mod_p_odd, _find_zeros_mod_p_2, _find_p_neighbor_from_vec, _basic_lemma
-from sage.quadratic_forms.ternary import _find_all_ternary_qf_by_level_disc, _find_a_ternary_qf_by_level_disc
 from sage.misc.prandom import randint
+from sage.quadratic_forms.quadratic_form import QuadraticForm
+from sage.quadratic_forms.ternary import (_basic_lemma,
+                                          _find_a_ternary_qf_by_level_disc,
+                                          _find_all_ternary_qf_by_level_disc,
+                                          _find_p_neighbor_from_vec,
+                                          _find_zeros_mod_p_2,
+                                          _find_zeros_mod_p_odd,
+                                          _reduced_ternary_form_eisenstein_with_matrix,
+                                          _reduced_ternary_form_eisenstein_without_matrix)
+
 from sage.rings.finite_rings.integer_mod import mod
-from sage.rings.ring import is_Ring
+from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring import polygens
+from sage.rings.ring import is_Ring
+from sage.structure.element import is_Vector, is_Matrix
+from sage.structure.sage_object import SageObject
 
 
 class TernaryQF(SageObject):
diff --git a/src/sage/rings/algebraic_closure_finite_field.py b/src/sage/rings/algebraic_closure_finite_field.py
index d45c3ec2cb0..273610c0afd 100644
--- a/src/sage/rings/algebraic_closure_finite_field.py
+++ b/src/sage/rings/algebraic_closure_finite_field.py
@@ -57,10 +57,9 @@
 from sage.misc.abstract_method import abstract_method
 from sage.misc.fast_methods import WithEqualityById
 
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.ring import Field
-from sage.structure.element import FieldElement
+from sage.structure.element import Element, FieldElement
 from sage.structure.richcmp import richcmp
 
 
@@ -91,7 +90,7 @@ def __init__(self, parent, value):
             and ``loads(dumps(x))``.
 
         """
-        if is_FiniteFieldElement(value):
+        if isinstance(value, Element) and isinstance(value.parent(), FiniteField):
             n = value.parent().degree()
         else:
             from sage.rings.integer import Integer
@@ -659,7 +658,7 @@ def _coerce_map_from_(self, other):
         """
         if other is self:
             return True
-        elif is_FiniteField(other) and self._subfield(other.degree()) is other:
+        elif isinstance(other, FiniteField) and self._subfield(other.degree()) is other:
             return True
         elif self._subfield(1).has_coerce_map_from(other):
             return True
@@ -1092,7 +1091,7 @@ def __init__(self, base_ring, name, category=None, lattice=None, use_database=Tr
             :meth:`AlgebraicClosureFiniteFieldElement.__init__`.
 
         """
-        if not (is_FiniteField(base_ring) and base_ring.is_prime_field()):
+        if not (isinstance(base_ring, FiniteField) and base_ring.is_prime_field()):
             raise NotImplementedError('algebraic closures of finite fields are only implemented for prime fields')
         from sage.rings.finite_rings.conway_polynomials import PseudoConwayLattice
         p = base_ring.characteristic()
diff --git a/src/sage/rings/finite_rings/__init__.py b/src/sage/rings/finite_rings/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/src/sage/rings/finite_rings/element_base.pyx b/src/sage/rings/finite_rings/element_base.pyx
index 29ab05dd8ba..4f785ebf181 100755
--- a/src/sage/rings/finite_rings/element_base.pyx
+++ b/src/sage/rings/finite_rings/element_base.pyx
@@ -25,20 +25,27 @@ from sage.misc.superseded import deprecated_function_alias
 
 def is_FiniteFieldElement(x):
     """
-    Returns if x is a finite field element.
+    Return True if ``x`` is a finite field element.
+
+    This function is deprecated.
 
     EXAMPLES::
 
         sage: from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         sage: is_FiniteFieldElement(1)
+        doctest:...: DeprecationWarning: the function is_FiniteFieldElement is deprecated; use isinstance(x, sage.structure.element.FieldElement) and x.parent().is_finite() instead
+        See https://github.com/sagemath/sage/issues/32664 for details.
         False
         sage: is_FiniteFieldElement(IntegerRing())
         False
         sage: is_FiniteFieldElement(GF(5)(2))
         True
     """
-    from sage.rings.finite_rings.finite_field_base import is_FiniteField
-    return isinstance(x, Element) and is_FiniteField(x.parent())
+    from sage.misc.superseded import deprecation
+    deprecation(32664, "the function is_FiniteFieldElement is deprecated; use isinstance(x, sage.structure.element.FieldElement) and x.parent().is_finite() instead")
+
+    from sage.rings.finite_rings.finite_field_base import FiniteField
+    return isinstance(x, Element) and isinstance(x.parent(), FiniteField)
 
 
 cdef class FiniteRingElement(CommutativeRingElement):
diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx
index 8a2d0ce94fa..06e57a04952 100644
--- a/src/sage/rings/finite_rings/finite_field_base.pyx
+++ b/src/sage/rings/finite_rings/finite_field_base.pyx
@@ -930,7 +930,7 @@ cdef class FiniteField(Field):
             sage: GF(3, 'a').is_prime_field()
             True
         """
-        return self.degree()==1
+        return self.degree() == 1
 
     def modulus(self):
         r"""
@@ -1356,7 +1356,7 @@ cdef class FiniteField(Field):
             return True
         if isinstance(R, sage.rings.abc.IntegerModRing) and self.characteristic().divides(R.characteristic()):
             return R.hom((self.one(),), check=False)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             if R is self:
                 return True
             from .residue_field import ResidueField_generic
@@ -2115,10 +2115,14 @@ def is_FiniteField(R):
     Return whether the implementation of ``R`` has the interface provided by
     the standard finite field implementation.
 
+    This function is deprecated.
+
     EXAMPLES::
 
         sage: from sage.rings.finite_rings.finite_field_base import is_FiniteField
         sage: is_FiniteField(GF(9,'a'))
+        doctest:...: DeprecationWarning: the function is_FiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) instead
+        See https://github.com/sagemath/sage/issues/32664 for details.
         True
         sage: is_FiniteField(GF(next_prime(10^10)))
         True
@@ -2128,4 +2132,6 @@ def is_FiniteField(R):
         sage: is_FiniteField(Integers(7))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(32664, "the function is_FiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) instead")
     return isinstance(R, FiniteField)
diff --git a/src/sage/rings/finite_rings/finite_field_constructor.py b/src/sage/rings/finite_rings/finite_field_constructor.py
index 8b51fd37b2e..048da483147 100644
--- a/src/sage/rings/finite_rings/finite_field_constructor.py
+++ b/src/sage/rings/finite_rings/finite_field_constructor.py
@@ -791,24 +791,32 @@ def create_object(self, version, key, **kwds):
 
 def is_PrimeFiniteField(x):
     """
-    Returns True if x is a prime finite field.
+    Returns True if ``x`` is a prime finite field.
+
+    This function is deprecated.
 
     EXAMPLES::
 
         sage: from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
         sage: is_PrimeFiniteField(QQ)
+        doctest:...: DeprecationWarning: the function is_PrimeFiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) and x.is_prime_field() instead
+        See https://github.com/sagemath/sage/issues/32664 for details.
         False
         sage: is_PrimeFiniteField(GF(7))
         True
-        sage: is_PrimeFiniteField(GF(7^2,'a'))
+        sage: is_PrimeFiniteField(GF(7^2, 'a'))
         False
-        sage: is_PrimeFiniteField(GF(next_prime(10^90,proof=False)))
+        sage: is_PrimeFiniteField(GF(next_prime(10^90, proof=False)))
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(32664, "the function is_PrimeFiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) and x.is_prime_field() instead")
+
     from .finite_field_prime_modn import FiniteField_prime_modn
     from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_generic
 
     return isinstance(x, FiniteField_prime_modn) or \
            (isinstance(x, FiniteField_generic) and x.degree() == 1)
 
+
 zech_log_bound = 2**16
diff --git a/src/sage/rings/finite_rings/finite_field_ntl_gf2e.py b/src/sage/rings/finite_rings/finite_field_ntl_gf2e.py
index e750f2fef5e..33ea3d1bcfc 100644
--- a/src/sage/rings/finite_rings/finite_field_ntl_gf2e.py
+++ b/src/sage/rings/finite_rings/finite_field_ntl_gf2e.py
@@ -52,6 +52,7 @@ def late_import():
     import sage.rings.polynomial.polynomial_element
     is_Polynomial = sage.rings.polynomial.polynomial_element.is_Polynomial
 
+
 class FiniteField_ntl_gf2e(FiniteField):
     """
     Finite Field of characteristic 2 and order `2^n`.
diff --git a/src/sage/rings/finite_rings/hom_finite_field.pyx b/src/sage/rings/finite_rings/hom_finite_field.pyx
index 86d2401ceec..44dc3450be8 100644
--- a/src/sage/rings/finite_rings/hom_finite_field.pyx
+++ b/src/sage/rings/finite_rings/hom_finite_field.pyx
@@ -106,7 +106,7 @@ from sage.rings.integer cimport Integer
 from sage.categories.homset import Hom
 from sage.structure.element cimport Element
 
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_base
 from sage.rings.morphism cimport RingHomomorphism, RingHomomorphism_im_gens, FrobeniusEndomorphism_generic
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 
@@ -227,9 +227,9 @@ cdef class FiniteFieldHomomorphism_generic(RingHomomorphism_im_gens):
         """
         domain = parent.domain()
         codomain = parent.codomain()
-        if not is_FiniteField(domain):
+        if not isinstance(domain, FiniteField_base):
             raise TypeError("The domain is not a finite field or does not provide the required interface for finite fields")
-        if not is_FiniteField(codomain):
+        if not isinstance(codomain, FiniteField_base):
             raise TypeError("The codomain is not a finite field or does not provide the required interface for finite fields")
         if domain.characteristic() != codomain.characteristic() or codomain.degree() % domain.degree() != 0:
             raise ValueError("No embedding of %s into %s" % (domain, codomain))
@@ -522,7 +522,7 @@ cdef class FrobeniusEndomorphism_finite_field(FrobeniusEndomorphism_generic):
             ...
             TypeError: The domain is not a finite field or does not provide the required interface for finite fields
         """
-        if not is_FiniteField(domain):
+        if not isinstance(domain, FiniteField_base):
             raise TypeError("The domain is not a finite field or does not provide the required interface for finite fields")
         try:
             n = Integer(n)
diff --git a/src/sage/rings/finite_rings/hom_prime_finite_field.pyx b/src/sage/rings/finite_rings/hom_prime_finite_field.pyx
index b24c8bbfb3e..617595ea383 100644
--- a/src/sage/rings/finite_rings/hom_prime_finite_field.pyx
+++ b/src/sage/rings/finite_rings/hom_prime_finite_field.pyx
@@ -33,7 +33,7 @@ from .hom_finite_field cimport SectionFiniteFieldHomomorphism_generic
 from .hom_finite_field cimport FiniteFieldHomomorphism_generic
 from .hom_finite_field cimport FrobeniusEndomorphism_finite_field
 
-from sage.rings.finite_rings.finite_field_base import FiniteField, is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.morphism cimport RingHomomorphism_im_gens
 
 
@@ -71,7 +71,7 @@ cdef class FiniteFieldHomomorphism_prime(FiniteFieldHomomorphism_generic):
             TypeError: The domain is not a finite prime field
         """
         domain = parent.domain()
-        if not is_FiniteField(domain) or not domain.is_prime_field():
+        if not isinstance(domain, FiniteField) or not domain.is_prime_field():
             raise TypeError("The domain is not a finite prime field")
         if section_class is None:
             section_class = SectionFiniteFieldHomomorphism_prime
@@ -100,7 +100,7 @@ cdef class FrobeniusEndomorphism_prime(FrobeniusEndomorphism_finite_field):
     fields (i.e. identity map :-).
     """
     def __init__(self, domain, power=1):
-        if not is_FiniteField(domain) or not domain.is_prime_field():
+        if not isinstance(domain, FiniteField) or not domain.is_prime_field():
             raise TypeError("The domain is not a finite prime field")
         FrobeniusEndomorphism_finite_field.__init__(self, Hom(domain, domain))
         self._order = 1
diff --git a/src/sage/rings/finite_rings/homset.py b/src/sage/rings/finite_rings/homset.py
index 0a7578a092e..ef629016983 100644
--- a/src/sage/rings/finite_rings/homset.py
+++ b/src/sage/rings/finite_rings/homset.py
@@ -37,7 +37,7 @@
 
 from sage.rings.homset import RingHomset_generic
 from sage.rings.finite_rings.hom_finite_field import FiniteFieldHomomorphism_generic
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.integer import Integer
 from sage.rings.morphism import RingHomomorphism_im_gens
 from sage.structure.sequence import Sequence
@@ -96,7 +96,7 @@ def __call__(self, im_gens, base_map=None, check=True):
             if self.domain().degree() == 1:
                 from sage.rings.finite_rings.hom_prime_finite_field import FiniteFieldHomomorphism_prime
                 return FiniteFieldHomomorphism_prime(self, im_gens, base_map=base_map, check=check)
-            if is_FiniteField(self.codomain()):
+            if isinstance(self.codomain(), FiniteField):
                 return FiniteFieldHomomorphism_generic(self, im_gens, base_map=base_map, check=check)
             # Currently, FiniteFieldHomomorphism_generic does not work if
             # the codomain is not derived from the finite field base class;
diff --git a/src/sage/rings/morphism.pyx b/src/sage/rings/morphism.pyx
index f7f83974425..204e6ddf474 100644
--- a/src/sage/rings/morphism.pyx
+++ b/src/sage/rings/morphism.pyx
@@ -3160,7 +3160,7 @@ def _tensor_product_ring(B, A):
         ...
         ValueError: term ordering must be global
     """
-    from .finite_rings.finite_field_base import is_FiniteField
+    from .finite_rings.finite_field_base import FiniteField
     from .number_field.number_field_base import is_NumberField
     from .polynomial.multi_polynomial_ring import is_MPolynomialRing
     from .polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
@@ -3178,7 +3178,7 @@ def _tensor_product_ring(B, A):
     def term_order(A):
         # univariate rings do not have a term order
         if (is_PolynomialRing(A) or is_PolynomialQuotientRing(A)
-            or ((is_NumberField(A) or is_FiniteField(A))
+            or ((is_NumberField(A) or isinstance(A, FiniteField))
                 and not A.is_prime_field())):
             return TermOrder('lex', 1)
         try:
@@ -3201,7 +3201,7 @@ def _tensor_product_ring(B, A):
         elif is_QuotientRing(A):
             to_R = A.ambient().hom(R_gens_A, R, check=False)
             return list(to_R(A.defining_ideal()).gens())
-        elif ((is_NumberField(A) or is_FiniteField(A))
+        elif ((is_NumberField(A) or isinstance(A, FiniteField))
               and not A.is_prime_field()):
             to_R = A.polynomial_ring().hom(R_gens_A, R, check=False)
             return [to_R(A.polynomial())]
diff --git a/src/sage/rings/padics/padic_template_element.pxi b/src/sage/rings/padics/padic_template_element.pxi
index ce9e7029002..a21494e5479 100644
--- a/src/sage/rings/padics/padic_template_element.pxi
+++ b/src/sage/rings/padics/padic_template_element.pxi
@@ -29,6 +29,7 @@ import sage.rings.finite_rings.integer_mod
 from cypari2.types cimport *
 from cypari2.gen cimport Gen as pari_gen
 from sage.libs.pari.convert_gmp cimport INT_to_mpz
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.padics.common_conversion cimport get_ordp, get_preccap
 from sage.rings.integer cimport Integer
 from sage.rings.infinity import infinity
@@ -37,6 +38,7 @@ from sage.rings.padics.precision_error import PrecisionError
 from sage.rings.padics.misc import trim_zeros
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.structure.element import canonical_coercion
+
 import itertools
 
 cdef long maxordp = (1L << (sizeof(long) * 8 - 2)) - 1
@@ -145,7 +147,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement):
         elif sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
             if not Integer(self.prime_pow.prime).divides(x.parent().order()):
                 raise TypeError("p does not divide modulus %s"%x.parent().order())
-        elif sage.rings.finite_rings.element_base.is_FiniteFieldElement(x):
+        elif isinstance(x, Element) and isinstance(x.parent(), FiniteField):
             k = self.parent().residue_field()
             if not k.has_coerce_map_from(x.parent()):
                 raise NotImplementedError("conversion from finite fields which do not embed into the residue field not implemented")
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index 88a25eae183..8b3a7549be1 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -4477,7 +4477,7 @@ cdef class Polynomial(CommutativePolynomial):
         if not (ch == 0 or is_prime(ch)):
             raise NotImplementedError("factorization of polynomials over rings with composite characteristic is not implemented")
 
-        from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+        from sage.rings.finite_rings.finite_field_base import FiniteField
 
         n = None
 
@@ -4487,7 +4487,7 @@ cdef class Polynomial(CommutativePolynomial):
             except PariError:
                 raise NotImplementedError
 
-        elif is_FiniteField(R):
+        elif isinstance(R, FiniteField):
             v = [x.__pari__("a") for x in self.list()]
             f = pari(v).Polrev()
             G = list(f.factor())
@@ -4755,7 +4755,7 @@ cdef class Polynomial(CommutativePolynomial):
         name = normalize_names(1, names)[0]
 
         from sage.rings.number_field.number_field_base import is_NumberField
-        from sage.rings.finite_rings.finite_field_base import is_FiniteField
+        from sage.rings.finite_rings.finite_field_base import FiniteField
 
         f = self.monic()            # Given polynomial, made monic
         F = f.parent().base_ring()  # Base field
@@ -4766,7 +4766,7 @@ cdef class Polynomial(CommutativePolynomial):
         if is_NumberField(F):
             from sage.rings.number_field.splitting_field import splitting_field
             return splitting_field(f, name, map, **kwds)
-        elif is_FiniteField(F):
+        elif isinstance(F, FiniteField):
             degree = lcm([f.degree() for f, _ in self.factor()])
             return F.extension(degree, name, map=map, **kwds)
 
diff --git a/src/sage/rings/polynomial/polynomial_ring_constructor.py b/src/sage/rings/polynomial/polynomial_ring_constructor.py
index 65e67cc3527..d2f03c205a3 100644
--- a/src/sage/rings/polynomial/polynomial_ring_constructor.py
+++ b/src/sage/rings/polynomial/polynomial_ring_constructor.py
@@ -26,7 +26,7 @@
 
 import sage.rings.abc
 from sage.rings.integer import Integer
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 
 from sage.misc.cachefunc import weak_cached_function
 import sage.misc.weak_dict
@@ -747,7 +747,7 @@ def _single_variate(base_ring, name, sparse=None, implementation=None, order=Non
             specialized = polynomial_ring.PolynomialRing_dense_mod_p
         elif n > 1:  # Specialized code breaks for n == 1
             specialized = polynomial_ring.PolynomialRing_dense_mod_n
-    elif is_FiniteField(base_ring):
+    elif isinstance(base_ring, FiniteField):
         specialized = polynomial_ring.PolynomialRing_dense_finite_field
     elif isinstance(base_ring, padic_base_leaves.pAdicFieldCappedRelative):
         specialized = polynomial_ring.PolynomialRing_dense_padic_field_capped_relative
diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
index 2b5bfd4bf94..f19415b34d3 100644
--- a/src/sage/rings/polynomial/polynomial_singular_interface.py
+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
@@ -44,7 +44,7 @@
 from sage.interfaces.singular import singular
 from sage.rings.rational_field import is_RationalField
 from sage.rings.function_field.function_field import RationalFunctionField
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.integer_ring import ZZ
 
 import sage.rings.finite_rings.finite_field_constructor
@@ -103,13 +103,13 @@ def _do_singular_init_(singular, base_ring, char, _vars, order):
 
     elif isinstance(base_ring, sage.rings.abc.IntegerModRing):
         char = base_ring.characteristic()
-        if sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring) and char <= 2147483647:
+        if isinstance(base_ring, FiniteField) and char <= 2147483647:
             return make_ring(str(char)), None
         if char.is_power_of(2):
             return make_ring(f"(integer,2,{char.nbits()-1})"), None
         return make_ring(f"(integer,{char})"), None
 
-    elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring):
+    elif isinstance(base_ring, FiniteField):
         # not the prime field!
         gen = str(base_ring.gen())
         R = make_ring(f"({char},{gen})")
@@ -148,7 +148,7 @@ def _do_singular_init_(singular, base_ring, char, _vars, order):
         if B.is_prime_field() or B is ZZ:
             return make_ring(f"({base_char},{gens})"), None
 
-        if is_FiniteField(B) and B.characteristic() <= 2147483647:
+        if isinstance(B, FiniteField) and B.characteristic() <= 2147483647:
             ext_gen = str(B.gen())
             _vars = '(' + ext_gen + ', ' + _vars[1:]
 
@@ -333,7 +333,7 @@ def _singular_(self, singular=singular):
             R._check_valid()
             if self.base_ring() is ZZ or self.base_ring().is_prime_field():
                 return R
-            if sage.rings.finite_rings.finite_field_constructor.is_FiniteField(self.base_ring()) or \
+            if isinstance(self.base_ring(), FiniteField) or \
                     (number_field.number_field_base.is_NumberField(self.base_ring()) and self.base_ring().is_absolute()):
                 R.set_ring()  # sorry for that, but needed for minpoly
                 if singular.eval('minpoly') != f"({self.__minpoly})":
@@ -427,14 +427,14 @@ def can_convert_to_singular(R):
                                   sage.rings.abc.RealField, sage.rings.abc.ComplexField,
                                   sage.rings.abc.RealDoubleField, sage.rings.abc.ComplexDoubleField))):
         return True
-    elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring):
+    elif isinstance(base_ring, FiniteField):
         return base_ring.characteristic() <= 2147483647
     elif number_field.number_field_base.is_NumberField(base_ring):
         return base_ring.is_absolute()
     elif sage.rings.fraction_field.is_FractionField(base_ring):
         B = base_ring.base_ring()
         return (B.is_prime_field() or B is ZZ
-                or (is_FiniteField(B) and B.characteristic() <= 2147483647))
+                or (isinstance(B, FiniteField) and B.characteristic() <= 2147483647))
     elif isinstance(base_ring, RationalFunctionField):
         return base_ring.constant_field().is_prime_field()
     else:
diff --git a/src/sage/schemes/affine/affine_homset.py b/src/sage/schemes/affine/affine_homset.py
index 98b3b3a8994..914e54f7148 100644
--- a/src/sage/schemes/affine/affine_homset.py
+++ b/src/sage/schemes/affine/affine_homset.py
@@ -41,7 +41,7 @@
 from sage.rings.rational_field import is_RationalField
 from sage.categories.fields import Fields
 from sage.categories.number_fields import NumberFields
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.schemes.generic.homset import SchemeHomset_points, SchemeHomset_generic
 
@@ -354,7 +354,7 @@ def points(self, **kwds):
                 raise TypeError("a positive bound B (= %s) must be specified"%B)
             from sage.schemes.affine.affine_rational_point import enum_affine_number_field
             return enum_affine_number_field(self, bound=B, tolerance=tol, precision=prec)
-        elif is_FiniteField(R):
+        elif isinstance(R, FiniteField):
             from sage.schemes.affine.affine_rational_point import enum_affine_finite_field
             return enum_affine_finite_field(self)
         else:
diff --git a/src/sage/schemes/affine/affine_morphism.py b/src/sage/schemes/affine/affine_morphism.py
index 38b71556ba2..b61b011f979 100644
--- a/src/sage/schemes/affine/affine_morphism.py
+++ b/src/sage/schemes/affine/affine_morphism.py
@@ -62,12 +62,11 @@
 from sage.arith.misc import GCD as gcd
 
 from sage.rings.integer import Integer
-from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
 from sage.rings.fraction_field import FractionField
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
 
@@ -229,7 +228,8 @@ def __init__(self, parent, polys, check=True):
         SchemeMorphism_polynomial.__init__(self, parent, polys, check)
 
         # used in _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(polys[0].base_ring())
+        R = polys[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
 
     def __call__(self, x, check=True):
         """
@@ -683,7 +683,7 @@ def as_dynamical_system(self):
         R = self.base_ring()
         if R not in _Fields:
             return DynamicalSystem_affine(list(self), self.domain())
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
                 return DynamicalSystem_affine_finite_field(list(self), self.domain())
         return DynamicalSystem_affine_field(list(self), self.domain())
 
diff --git a/src/sage/schemes/affine/affine_space.py b/src/sage/schemes/affine/affine_space.py
index ba56ef9fc8d..52c13b29068 100644
--- a/src/sage/schemes/affine/affine_space.py
+++ b/src/sage/schemes/affine/affine_space.py
@@ -17,7 +17,7 @@
 from sage.rings.rational_field import is_RationalField
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.categories.map import Map
 from sage.categories.fields import Fields
 from sage.categories.homset import Hom
@@ -132,7 +132,7 @@ def AffineSpace(n, R=None, names=None, ambient_projective_space=None,
         from sage.schemes.projective.projective_space import ProjectiveSpace
         ambient_projective_space = ProjectiveSpace(n, R)
     if R in _Fields:
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return AffineSpace_finite_field(n, R, names,
                                             ambient_projective_space, default_embedding_index)
         else:
@@ -270,12 +270,12 @@ def rational_points(self, F=None):
             TypeError: second argument (= Integer Ring) must be a finite field
         """
         if F is None:
-            if not is_FiniteField(self.base_ring()):
-                raise TypeError("base ring (= %s) must be a finite field"%self.base_ring())
-            return [ P for P in self ]
-        elif not is_FiniteField(F):
-            raise TypeError("second argument (= %s) must be a finite field"%F)
-        return [ P for P in self.base_extend(F) ]
+            if not isinstance(self.base_ring(), FiniteField):
+                raise TypeError("base ring (= %s) must be a finite field" % self.base_ring())
+            return [P for P in self]
+        elif not isinstance(F, FiniteField):
+            raise TypeError("second argument (= %s) must be a finite field" % F)
+        return [P for P in self.base_extend(F)]
 
     def __eq__(self, right):
         """
diff --git a/src/sage/schemes/curves/constructor.py b/src/sage/schemes/curves/constructor.py
index c3ff0fa9a42..88f9b95701f 100644
--- a/src/sage/schemes/curves/constructor.py
+++ b/src/sage/schemes/curves/constructor.py
@@ -38,7 +38,7 @@
 
 from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 
 from sage.rings.rational_field import QQ
 
@@ -294,7 +294,7 @@ def Curve(F, A=None):
 
     if is_AffineSpace(A):
         if n != 2:
-            if is_FiniteField(k):
+            if isinstance(k, FiniteField):
                 if A.coordinate_ring().ideal(F).is_prime():
                     return IntegralAffineCurve_finite_field(A, F)
             if k in Fields():
@@ -307,7 +307,7 @@ def Curve(F, A=None):
             raise TypeError("need a single nonconstant polynomial to define a plane curve")
 
         F = F[0]
-        if is_FiniteField(k):
+        if isinstance(k, FiniteField):
             if _is_irreducible_and_reduced(F):
                 return IntegralAffinePlaneCurve_finite_field(A, F)
             return AffinePlaneCurve_finite_field(A, F)
@@ -321,7 +321,7 @@ def Curve(F, A=None):
         if n != 2:
             if not all(f.is_homogeneous() for f in F):
                 raise TypeError("polynomials defining a curve in a projective space must be homogeneous")
-            if is_FiniteField(k):
+            if isinstance(k, FiniteField):
                 if A.coordinate_ring().ideal(F).is_prime():
                     return IntegralProjectiveCurve_finite_field(A, F)
             if k in Fields():
@@ -339,7 +339,7 @@ def Curve(F, A=None):
         if not F.is_homogeneous():
             raise TypeError("{} is not a homogeneous polynomial".format(F))
 
-        if is_FiniteField(k):
+        if isinstance(k, FiniteField):
             if _is_irreducible_and_reduced(F):
                 return IntegralProjectivePlaneCurve_finite_field(A, F)
             return ProjectivePlaneCurve_finite_field(A, F)
diff --git a/src/sage/schemes/cyclic_covers/constructor.py b/src/sage/schemes/cyclic_covers/constructor.py
index 32bdf239b99..0a8926d7db6 100644
--- a/src/sage/schemes/cyclic_covers/constructor.py
+++ b/src/sage/schemes/cyclic_covers/constructor.py
@@ -8,9 +8,10 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_element import Polynomial
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
 from sage.schemes.affine.affine_space import AffineSpace
+
 from .cycliccover_generic import CyclicCover_generic
 from .cycliccover_finite_field import CyclicCover_finite_field
 
@@ -127,7 +128,7 @@ def CyclicCover(r, f, names=None, check_smooth=True):
         names = ["x", "y"]
     A2 = AffineSpace(2, R, names=names)
 
-    if is_FiniteField(R):
+    if isinstance(R, FiniteField):
         return CyclicCover_finite_field(A2, r, f, names=names)
     else:
         return CyclicCover_generic(A2, r, f, names=names)
diff --git a/src/sage/schemes/elliptic_curves/constructor.py b/src/sage/schemes/elliptic_curves/constructor.py
index d924bd8f45c..8d1a7ddf363 100644
--- a/src/sage/schemes/elliptic_curves/constructor.py
+++ b/src/sage/schemes/elliptic_curves/constructor.py
@@ -27,7 +27,7 @@
 
 import sage.rings.abc
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.number_field.number_field import is_NumberField
 from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.rings.ring import is_Ring
@@ -477,7 +477,7 @@ def create_object(self, version, key, **kwds):
         elif isinstance(R, sage.rings.abc.pAdicField):
             from .ell_padic_field import EllipticCurve_padic_field
             return EllipticCurve_padic_field(R, x)
-        elif is_FiniteField(R) or (isinstance(R, sage.rings.abc.IntegerModRing) and R.characteristic().is_prime()):
+        elif isinstance(R, FiniteField) or (isinstance(R, sage.rings.abc.IntegerModRing) and R.characteristic().is_prime()):
             from .ell_finite_field import EllipticCurve_finite_field
             return EllipticCurve_finite_field(R, x)
         elif R in _Fields:
diff --git a/src/sage/schemes/elliptic_curves/ell_finite_field.py b/src/sage/schemes/elliptic_curves/ell_finite_field.py
index 9da8cc3acfd..d0279e553f1 100644
--- a/src/sage/schemes/elliptic_curves/ell_finite_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_finite_field.py
@@ -31,7 +31,7 @@
 from sage.arith.misc import binomial, GCD as gcd
 from sage.groups.additive_abelian.additive_abelian_wrapper import AdditiveAbelianGroupWrapper
 from sage.misc.cachefunc import cached_method
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
@@ -39,6 +39,7 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.schemes.curves.projective_curve import Hasse_bounds
 from sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field import HyperellipticCurve_finite_field
+from sage.structure.element import Element
 
 from . import ell_point
 from .constructor import EllipticCurve
@@ -2102,7 +2103,7 @@ def is_j_supersingular(j, proof=True):
         sage: [p for p in prime_range(100) if is_j_supersingular(GF(p)(123456))]
         [2, 3, 59, 89]
     """
-    if not is_FiniteFieldElement(j):
+    if not (isinstance(j, Element) and isinstance(j.parent(), FiniteField)):
         raise ValueError("%s must be an element of a finite field" % j)
 
     F = j.parent()
diff --git a/src/sage/schemes/generic/algebraic_scheme.py b/src/sage/schemes/generic/algebraic_scheme.py
index 9e1fe6b4b56..6391bc54eeb 100644
--- a/src/sage/schemes/generic/algebraic_scheme.py
+++ b/src/sage/schemes/generic/algebraic_scheme.py
@@ -132,7 +132,7 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.qqbar import QQbar
 from sage.rings.rational_field import is_RationalField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.number_field.order import is_NumberFieldOrder
 
 from sage.misc.latex import latex
@@ -886,7 +886,7 @@ def rational_points(self, **kwds):
         if bound == 0:
             if is_RationalField(F):
                 raise TypeError("A positive bound (= %s) must be specified."%bound)
-            if not is_FiniteField(F):
+            if not isinstance(F, FiniteField):
                 raise TypeError("Argument F (= %s) must be a finite field."%F)
         pts = []
         for P in self.ambient_space().rational_points(F):
diff --git a/src/sage/schemes/hyperelliptic_curves/constructor.py b/src/sage/schemes/hyperelliptic_curves/constructor.py
index e73efa85558..afd87af8cb3 100644
--- a/src/sage/schemes/hyperelliptic_curves/constructor.py
+++ b/src/sage/schemes/hyperelliptic_curves/constructor.py
@@ -23,10 +23,10 @@
 from .hyperelliptic_g2 import HyperellipticCurve_g2
 
 import sage.rings.abc
-from sage.rings.rational_field import is_RationalField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.polynomial.polynomial_element import Polynomial
 
+from sage.rings.finite_rings.finite_field_base import FiniteField
+from sage.rings.polynomial.polynomial_element import Polynomial
+from sage.rings.rational_field import is_RationalField
 from sage.structure.dynamic_class import dynamic_class
 
 
@@ -249,7 +249,11 @@ def HyperellipticCurve(f, h=0, names=None, PP=None, check_squarefree=True):
 
     genus_classes = {2: HyperellipticCurve_g2}
 
-    is_pAdicField = lambda x: isinstance(x, sage.rings.abc.pAdicField)
+    def is_FiniteField(x):
+        return isinstance(x, FiniteField)
+
+    def is_pAdicField(x):
+        return isinstance(x, sage.rings.abc.pAdicField)
 
     fields = [
         ("FiniteField", is_FiniteField, HyperellipticCurve_finite_field),
diff --git a/src/sage/schemes/plane_conics/constructor.py b/src/sage/schemes/plane_conics/constructor.py
index abff2935854..258476ca09c 100644
--- a/src/sage/schemes/plane_conics/constructor.py
+++ b/src/sage/schemes/plane_conics/constructor.py
@@ -27,20 +27,18 @@
 from sage.matrix.constructor import Matrix
 from sage.modules.free_module_element import vector
 from sage.quadratic_forms.quadratic_form import is_QuadraticForm
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-
 from sage.rings.ring import IntegralDomain
 from sage.rings.rational_field import is_RationalField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.polynomial.multi_polynomial import MPolynomial
-from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import is_FractionField
-
 from sage.rings.number_field.number_field import is_NumberField
-from sage.schemes.projective.projective_space import ProjectiveSpace
-from sage.schemes.projective.projective_point import SchemeMorphism_point_projective_field
+from sage.rings.polynomial.multi_polynomial import MPolynomial
+from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.schemes.affine.affine_point import SchemeMorphism_point_affine
+from sage.schemes.projective.projective_point import SchemeMorphism_point_projective_field
+from sage.schemes.projective.projective_space import ProjectiveSpace
 from sage.structure.all import Sequence
 from sage.structure.element import is_Matrix
 
@@ -233,7 +231,7 @@ def Conic(base_field, F=None, names=None, unique=True):
 
     if F.parent().ngens() == 3:
         P2 = ProjectiveSpace(2, base_field, names)
-        if is_FiniteField(base_field):
+        if isinstance(base_field, FiniteField):
             return ProjectiveConic_finite_field(P2, F)
         if is_RationalField(base_field):
             return ProjectiveConic_rational_field(P2, F)
diff --git a/src/sage/schemes/product_projective/homset.py b/src/sage/schemes/product_projective/homset.py
index 28aa566bb73..b56eccb968e 100644
--- a/src/sage/schemes/product_projective/homset.py
+++ b/src/sage/schemes/product_projective/homset.py
@@ -22,7 +22,7 @@
 from sage.categories.number_fields import NumberFields
 from sage.misc.mrange import xmrange
 from sage.misc.misc_c import prod
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.rational_field import is_RationalField
 from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme
 from sage.schemes.generic.homset import SchemeHomset_points
@@ -228,7 +228,7 @@ def points(self, **kwds):
                 raise TypeError("a positive bound B (= %s) must be specified"%B)
             from sage.schemes.product_projective.rational_point import enum_product_projective_number_field
             return enum_product_projective_number_field(self, bound=B)
-        elif is_FiniteField(R):
+        elif isinstance(R, FiniteField):
             from sage.schemes.product_projective.rational_point import enum_product_projective_finite_field
             return enum_product_projective_finite_field(self)
         else:
diff --git a/src/sage/schemes/product_projective/space.py b/src/sage/schemes/product_projective/space.py
index 604adcc8a41..4597d1c3798 100644
--- a/src/sage/schemes/product_projective/space.py
+++ b/src/sage/schemes/product_projective/space.py
@@ -45,7 +45,7 @@
 from sage.rings.integer import Integer
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.categories.fields import Fields
 from sage.categories.commutative_rings import CommutativeRings
 from sage.rings.polynomial.polydict import ETuple
@@ -137,7 +137,7 @@ def ProductProjectiveSpaces(n, R=None, names='x'):
                 raise AttributeError("components must be over the same base ring")
             N.append(PS.dimension_relative())
             names += PS.variable_names()
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             X = ProductProjectiveSpaces_finite_field(N, R, names)
         elif R in Fields():
             X = ProductProjectiveSpaces_field(N, R, names)
@@ -162,7 +162,7 @@ def ProductProjectiveSpaces(n, R=None, names='x'):
             else:
                 n_vars = sum(1+d for d in n)
                 names = normalize_names(n_vars, name_list)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             X = ProductProjectiveSpaces_finite_field(n, R, names)
         elif R in Fields():
             X = ProductProjectiveSpaces_field(n, R, names)
@@ -1302,6 +1302,6 @@ def rational_points(self, F=None):
         """
         if F is None:
             return list(self)
-        elif not is_FiniteField(F):
+        elif not isinstance(F, FiniteField):
             raise TypeError("second argument (= %s) must be a finite field"%F)
         return list(self.base_extend(F))
diff --git a/src/sage/schemes/projective/projective_homset.py b/src/sage/schemes/projective/projective_homset.py
index 3ffd4a6b6e4..3ee0b78876e 100644
--- a/src/sage/schemes/projective/projective_homset.py
+++ b/src/sage/schemes/projective/projective_homset.py
@@ -47,7 +47,7 @@
 from sage.rings.rational_field import is_RationalField
 from sage.categories.fields import Fields
 from sage.categories.number_fields import NumberFields
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme
 from copy import copy
@@ -284,7 +284,7 @@ def points(self, **kwds):
                 raise TypeError("a positive bound B (= %s) must be specified"%B)
             from sage.schemes.projective.projective_rational_point import enum_projective_number_field
             return enum_projective_number_field(self, bound=B, tolerance=tol, precision=prec)
-        elif is_FiniteField(R):
+        elif isinstance(R, FiniteField):
             from sage.schemes.projective.projective_rational_point import enum_projective_finite_field
             return enum_projective_finite_field(self.extended_codomain())
         else:
diff --git a/src/sage/schemes/projective/projective_morphism.py b/src/sage/schemes/projective/projective_morphism.py
index facc90bb53d..9c608f67a48 100644
--- a/src/sage/schemes/projective/projective_morphism.py
+++ b/src/sage/schemes/projective/projective_morphism.py
@@ -73,8 +73,7 @@
 import sage.rings.abc
 from sage.rings.integer import Integer
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.fraction_field import FractionField
 from sage.rings.integer_ring import ZZ
@@ -275,7 +274,8 @@ def __init__(self, parent, polys, check=True):
 
         SchemeMorphism_polynomial.__init__(self, parent, polys, check)
 
-        self._is_prime_finite_field = is_PrimeFiniteField(polys[0].base_ring())
+        R = polys[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
 
     def __call__(self, x, check=True):
         r"""
@@ -728,7 +728,7 @@ def as_dynamical_system(self):
         R = self.base_ring()
         if R not in _Fields:
             return DynamicalSystem_projective(list(self), self.domain())
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return DynamicalSystem_projective_finite_field(list(self), self.domain())
         return DynamicalSystem_projective_field(list(self), self.domain())
 
@@ -1007,7 +1007,7 @@ def normalize_coordinates(self, **kwds):
         # scales by 1/gcd of the coefficients.
         if R in _NumberFields:
             O = R.maximal_order()
-        elif is_FiniteField(R):
+        elif isinstance(R, FiniteField):
             O = R
         elif isinstance(R, QuotientRing_generic):
             O = R.ring()
diff --git a/src/sage/schemes/projective/projective_space.py b/src/sage/schemes/projective/projective_space.py
index 670304af237..e215da942e1 100644
--- a/src/sage/schemes/projective/projective_space.py
+++ b/src/sage/schemes/projective/projective_space.py
@@ -81,7 +81,7 @@
 
 from sage.arith.misc import gcd, binomial
 
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
@@ -256,7 +256,7 @@ def ProjectiveSpace(n, R=None, names=None):
     if R is None:
         R = ZZ  # default is the integers
     if R in _Fields:
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return ProjectiveSpace_finite_field(n, R, names)
         if is_RationalField(R):
             return ProjectiveSpace_rational_field(n, R, names)
@@ -2253,7 +2253,7 @@ def rational_points(self, F=None):
         """
         if F is None:
             return [P for P in self]
-        elif not is_FiniteField(F):
+        elif not isinstance(F, FiniteField):
             raise TypeError("second argument (= %s) must be a finite field" % F)
         return [P for P in self.base_extend(F)]
 
diff --git a/src/sage/schemes/projective/projective_subscheme.py b/src/sage/schemes/projective/projective_subscheme.py
index 8a93cb30d83..4a178c53766 100644
--- a/src/sage/schemes/projective/projective_subscheme.py
+++ b/src/sage/schemes/projective/projective_subscheme.py
@@ -29,7 +29,7 @@
 from sage.matrix.constructor import matrix
 
 from sage.rings.integer_ring import ZZ
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import is_RationalField
 
@@ -982,7 +982,7 @@ def dual(self):
         from sage.libs.singular.function_factory import ff
 
         K = self.base_ring()
-        if not (is_RationalField(K) or is_FiniteField(K)):
+        if not (is_RationalField(K) or isinstance(K, FiniteField)):
             raise NotImplementedError("base ring must be QQ or a finite field")
         I = self.defining_ideal()
         m = I.ngens()
diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx
index 2bfb28f249e..f1547a92301 100644
--- a/src/sage/symbolic/ring.pyx
+++ b/src/sage/symbolic/ring.pyx
@@ -217,7 +217,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
             from sage.rings.complex_mpfr import ComplexField
             from sage.rings.infinity import InfinityRing, UnsignedInfinityRing
             from sage.rings.real_lazy import RLF, CLF
-            from sage.rings.finite_rings.finite_field_base import is_FiniteField
+            from sage.rings.finite_rings.finite_field_base import FiniteField
 
             from sage.interfaces.maxima import Maxima
 
@@ -234,8 +234,8 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
                                     sage.rings.abc.ComplexIntervalField,
                                     sage.rings.abc.RealBallField,
                                     sage.rings.abc.ComplexBallField,
-                                    sage.rings.abc.IntegerModRing))
-                  or is_FiniteField(R)):
+                                    sage.rings.abc.IntegerModRing,
+                                    FiniteField))):
                 return True
             elif isinstance(R, GenericSymbolicSubring):
                 return True