diff --git a/src/sage/rings/abc.pyx b/src/sage/rings/abc.pyx
index eb471a6c34d..e776559d81a 100644
--- a/src/sage/rings/abc.pyx
+++ b/src/sage/rings/abc.pyx
@@ -10,6 +10,22 @@ cdef class RealField(Field):
     pass
 
 
+class RealBallField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.real_arb.RealBallField`.
+    """
+
+    pass
+
+
+cdef class RealIntervalField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.real_mpfi.RealIntervalField_class`.
+    """
+
+    pass
+
+
 cdef class RealDoubleField(Field):
     r"""
     Abstract base class for :class:`~sage.rings.real_double.RealDoubleField_class`.
@@ -26,6 +42,22 @@ cdef class ComplexField(Field):
     pass
 
 
+class ComplexBallField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.complex_arb.ComplexBallField`.
+    """
+
+    pass
+
+
+class ComplexIntervalField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.complex_interval_field.ComplexIntervalField_class`.
+    """
+
+    pass
+
+
 cdef class ComplexDoubleField(Field):
     r"""
     Abstract base class for :class:`~sage.rings.complex_double.ComplexDoubleField_class`.
diff --git a/src/sage/rings/complex_arb.pyx b/src/sage/rings/complex_arb.pyx
index 977580a2926..bc3b7f8e792 100644
--- a/src/sage/rings/complex_arb.pyx
+++ b/src/sage/rings/complex_arb.pyx
@@ -147,6 +147,7 @@ from cysignals.signals cimport sig_on, sig_str, sig_off, sig_error
 
 import sage.categories.fields
 
+cimport sage.rings.abc
 cimport sage.rings.rational
 
 from cpython.float cimport PyFloat_AS_DOUBLE
@@ -302,6 +303,7 @@ cdef int acb_calc_func_callback(acb_ptr out, const acb_t inp, void * param,
     finally:
         sig_on()
 
+
 class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
     r"""
     An approximation of the field of complex numbers using pairs of mid-rad
diff --git a/src/sage/rings/complex_interval_field.py b/src/sage/rings/complex_interval_field.py
index cee580b22a3..05758d9956b 100644
--- a/src/sage/rings/complex_interval_field.py
+++ b/src/sage/rings/complex_interval_field.py
@@ -40,6 +40,7 @@
 from .integer_ring import ZZ
 from .rational_field import QQ
 from .ring import Field
+import sage.rings.abc
 from . import integer
 from . import complex_interval
 import weakref
@@ -55,13 +56,20 @@ def is_ComplexIntervalField(x):
     EXAMPLES::
 
         sage: from sage.rings.complex_interval_field import is_ComplexIntervalField as is_CIF
+        doctest:warning...
+        DeprecationWarning: is_ComplexIntervalField is deprecated;
+        use isinstance(..., sage.rings.abc.ComplexIntervalField) instead
+        See https://trac.sagemath.org/32612 for details.
         sage: is_CIF(CIF)
         True
         sage: is_CIF(CC)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(32612, 'is_ComplexIntervalField is deprecated; use isinstance(..., sage.rings.abc.ComplexIntervalField) instead')
     return isinstance(x, ComplexIntervalField_class)
 
+
 cache = {}
 def ComplexIntervalField(prec=53, names=None):
     """
@@ -93,7 +101,7 @@ def ComplexIntervalField(prec=53, names=None):
     return C
 
 
-class ComplexIntervalField_class(Field):
+class ComplexIntervalField_class(sage.rings.abc.ComplexIntervalField):
     """
     The field of complex (interval) numbers.
 
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index f8cadacb0d0..4b188823ac3 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -9945,9 +9945,8 @@ def hilbert_symbol(self, a, b, P = None):
             if P.domain() is not self:
                 raise ValueError("Domain of P (=%s) should be self (=%s) in self.hilbert_symbol" % (P, self))
             codom = P.codomain()
-            from sage.rings.complex_interval_field import is_ComplexIntervalField
             from sage.rings.all import (AA, QQbar)
-            if isinstance(codom, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField)) or is_ComplexIntervalField(codom) or \
+            if isinstance(codom, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField, sage.rings.abc.ComplexIntervalField)) or \
                                          codom is QQbar:
                 if P(self.gen()).imag() == 0:
                     raise ValueError("Possibly real place (=%s) given as complex embedding in hilbert_symbol. Is it real or complex?" % P)
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index f7807221d55..0d2cfda744d 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -92,7 +92,7 @@ CC = ComplexField()
 
 from sage.rings.real_double import RDF
 from sage.rings.complex_double import CDF
-from sage.rings.real_mpfi import is_RealIntervalField
+import sage.rings.abc
 
 from sage.structure.coerce cimport coercion_model
 from sage.structure.element import coerce_binop
@@ -8030,7 +8030,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             # and complex root isolation and for p-adic factorization
             if (is_IntegerRing(K) or is_RationalField(K)
                 or is_AlgebraicRealField(K)) and \
-                (is_AlgebraicRealField(L) or is_RealIntervalField(L)):
+                (is_AlgebraicRealField(L) or isinstance(L, sage.rings.abc.RealIntervalField)):
 
                 from sage.rings.polynomial.real_roots import real_roots
 
@@ -8060,11 +8060,11 @@ cdef class Polynomial(CommutativeAlgebraElement):
 
             if (is_IntegerRing(K) or is_RationalField(K)
                 or is_AlgebraicField_common(K) or input_gaussian) and \
-                (is_ComplexIntervalField(L) or is_AlgebraicField_common(L)):
+                (isinstance(L, sage.rings.abc.ComplexIntervalField) or is_AlgebraicField_common(L)):
 
                 from sage.rings.polynomial.complex_roots import complex_roots
 
-                if is_ComplexIntervalField(L):
+                if isinstance(L, sage.rings.abc.ComplexIntervalField):
                     rts = complex_roots(self, min_prec=L.prec())
                 elif is_AlgebraicField(L):
                     rts = complex_roots(self, retval='algebraic')
diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index a63315f93b1..a36b5de3c72 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -5013,7 +5013,7 @@ def interval_exact(self, field):
             sage: (a - b).interval_exact(CIF)
             0
         """
-        if not is_ComplexIntervalField(field):
+        if not isinstance(field, sage.rings.abc.ComplexIntervalField):
             raise ValueError("AlgebraicNumber interval_exact requires a ComplexIntervalField")
         rfld = field._real_field()
         re = self.real().interval_exact(rfld)
@@ -5910,7 +5910,7 @@ def _complex_mpfr_field_(self, field):
             sage: AA(golden_ratio)._complex_mpfr_field_(ComplexField(100))
             1.6180339887498948482045868344
         """
-        if is_ComplexIntervalField(field):
+        if isinstance(field, sage.rings.abc.ComplexIntervalField):
             return field(self.interval(field._real_field()))
         else:
             return field(self.real_number(field._real_field()))
diff --git a/src/sage/rings/real_arb.pyx b/src/sage/rings/real_arb.pyx
index 66a9d7bda06..43b6b6da5fd 100644
--- a/src/sage/rings/real_arb.pyx
+++ b/src/sage/rings/real_arb.pyx
@@ -219,6 +219,7 @@ from sage.libs.mpfr cimport MPFR_RNDN, MPFR_RNDU, MPFR_RNDD, MPFR_RNDZ
 
 from sage.structure.element cimport Element, ModuleElement, RingElement
 from sage.rings.ring cimport Field
+import sage.rings.abc
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 from sage.rings.real_double cimport RealDoubleElement
@@ -320,7 +321,7 @@ cdef int arb_to_mpfi(mpfi_t target, arb_t source, const long precision) except -
         mpfr_clear(right)
 
 
-class RealBallField(UniqueRepresentation, Field):
+class RealBallField(UniqueRepresentation, sage.rings.abc.RealBallField):
     r"""
     An approximation of the field of real numbers using mid-rad intervals, also
     known as balls.
diff --git a/src/sage/rings/real_interval_absolute.pyx b/src/sage/rings/real_interval_absolute.pyx
index 2b193145eb3..16a275aab2b 100644
--- a/src/sage/rings/real_interval_absolute.pyx
+++ b/src/sage/rings/real_interval_absolute.pyx
@@ -185,7 +185,7 @@ cdef class RealIntervalAbsoluteField_class(Field):
         """
         if isinstance(R, RealIntervalAbsoluteField_class):
             return self._absprec < (<RealIntervalAbsoluteField_class>R)._absprec
-        elif is_RealIntervalField(R):
+        elif isinstance(R, sage.rings.abc.RealIntervalField):
             return True
         else:
             return RR_min_prec.has_coerce_map_from(R)
diff --git a/src/sage/rings/real_mpfi.pxd b/src/sage/rings/real_mpfi.pxd
index c32dcc959d0..5466a5f575f 100644
--- a/src/sage/rings/real_mpfi.pxd
+++ b/src/sage/rings/real_mpfi.pxd
@@ -2,7 +2,7 @@ from sage.libs.mpfr.types cimport mpfr_prec_t
 from sage.libs.mpfi.types cimport mpfi_t
 
 from sage.rings.ring cimport Field
-
+cimport sage.rings.abc
 from sage.structure.element cimport RingElement
 
 from .rational cimport Rational
@@ -10,7 +10,7 @@ from .real_mpfr cimport RealField_class
 
 cdef class RealIntervalFieldElement(RingElement)  # forward decl
 
-cdef class RealIntervalField_class(Field):
+cdef class RealIntervalField_class(sage.rings.abc.RealIntervalField):
     cdef mpfr_prec_t __prec
     cdef bint sci_not
     # Cache RealField instances for the lower, upper, and middle bounds.
diff --git a/src/sage/rings/real_mpfi.pyx b/src/sage/rings/real_mpfi.pyx
index 2bfdc5f2512..ce83e1ddf4e 100644
--- a/src/sage/rings/real_mpfi.pyx
+++ b/src/sage/rings/real_mpfi.pyx
@@ -345,7 +345,7 @@ cpdef RealIntervalField_class RealIntervalField(prec=53, sci_not=False):
         return R
 
 
-cdef class RealIntervalField_class(Field):
+cdef class RealIntervalField_class(sage.rings.abc.RealIntervalField):
     """
     Class of the real interval field.
 
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index 638b0305a0c..576e670d0eb 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -85,6 +85,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.rings.abc
 from .ell_field import EllipticCurve_field
 from .ell_generic import is_EllipticCurve
 from .ell_point import EllipticCurvePoint_number_field
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index be2bbd065a8..de14f5c2d22 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -3565,8 +3565,8 @@ cdef class Expression(CommutativeRingElement):
                 else:
                     domain = RIF
         else:
-            is_interval = (is_RealIntervalField(domain)
-                           or is_ComplexIntervalField(domain)
+            is_interval = (isinstance(domain, (sage.rings.abc.RealIntervalField,
+                                               sage.rings.abc.ComplexIntervalField))
                            or is_AlgebraicField(domain)
                            or is_AlgebraicRealField(domain))
         zero = domain(0)
@@ -3620,7 +3620,7 @@ cdef class Expression(CommutativeRingElement):
                         eq_count += <bint>val.contains_zero()
                 except (TypeError, ValueError, ArithmeticError, AttributeError) as ex:
                     errors += 1
-                    if k == errors > 3 and is_ComplexIntervalField(domain):
+                    if k == errors > 3 and isinstance(domain, sage.rings.abc.ComplexIntervalField):
                         domain = RIF.to_prec(domain.prec())
                     # we are plugging in random values above, don't be surprised
                     # if something goes wrong...
diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx
index 7b90d56d0e3..0f3a8b9fc07 100644
--- a/src/sage/symbolic/ring.pyx
+++ b/src/sage/symbolic/ring.pyx
@@ -231,9 +231,10 @@ cdef class SymbolicRing(CommutativeRing):
                 base = R.base_ring()
                 return base is not self and self.has_coerce_map_from(base)
             elif (R is InfinityRing or R is UnsignedInfinityRing
-                  or is_RealIntervalField(R) or is_ComplexIntervalField(R)
-                  or isinstance(R, RealBallField)
-                  or isinstance(R, ComplexBallField)
+                  or isinstance(R, (sage.rings.abc.RealIntervalField,
+                                    sage.rings.abc.ComplexIntervalField,
+                                    sage.rings.abc.RealBallField,
+                                    sage.rings.abc.ComplexBallField))
                   or is_IntegerModRing(R) or is_FiniteField(R)):
                 return True
             elif isinstance(R, GenericSymbolicSubring):
diff --git a/src/sage/symbolic/subring.py b/src/sage/symbolic/subring.py
index 060ad32a5ed..c1eb48e16ae 100644
--- a/src/sage/symbolic/subring.py
+++ b/src/sage/symbolic/subring.py
@@ -97,6 +97,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+import sage.rings.abc
 from .ring import SymbolicRing, SR
 from sage.categories.pushout import ConstructionFunctor
 from sage.structure.factory import UniqueFactory
@@ -412,8 +413,6 @@ def _coerce_map_from_(self, P):
             return False
 
         from sage.rings.all import RLF, CLF, AA, QQbar, InfinityRing
-        from sage.rings.real_mpfi import is_RealIntervalField
-        from sage.rings.complex_interval_field import is_ComplexIntervalField
 
         if isinstance(P, type):
             return SR._coerce_map_from_(P)
@@ -425,7 +424,8 @@ def _coerce_map_from_(self, P):
             return True
 
         elif (P is InfinityRing or
-              is_RealIntervalField(P) or is_ComplexIntervalField(P)):
+              isinstance(P, (sage.rings.abc.RealIntervalField,
+                             sage.rings.abc.ComplexIntervalField))):
             return True
 
         elif P._is_numerical():