diff --git a/src/sage/rings/integer_ring.pyx b/src/sage/rings/integer_ring.pyx
index ea76b578bb4..76ea3c4f317 100644
--- a/src/sage/rings/integer_ring.pyx
+++ b/src/sage/rings/integer_ring.pyx
@@ -51,6 +51,7 @@ include "cysignals/signals.pxi"
 
 from cpython.int cimport *
 from cpython.list cimport *
+from cpython.object cimport Py_NE
 
 import sage.rings.infinity
 import sage.rings.rational
@@ -64,7 +65,9 @@ from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.structure.coerce cimport is_numpy_type
 from sage.structure.parent_gens import ParentWithGens
 from sage.structure.parent cimport Parent
+from sage.structure.sage_object cimport rich_to_bool
 from sage.structure.sequence import Sequence
+
 from sage.misc.misc_c import prod
 from sage.misc.randstate cimport randstate, current_randstate, SAGE_RAND_MAX
 from sage.libs.ntl.convert cimport ZZ_to_mpz
@@ -369,25 +372,13 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
             sage: ZZ != QQ
             True
         """
-        return (<Parent>left)._richcmp(right, op)
-
-    cpdef int _cmp_(left, right) except -2:
-        """
-        Compare ``left`` and ``right``.
-
-        TESTS::
+        if left is right:
+            return rich_to_bool(op, 0)
 
-            sage: from sage.rings.integer_ring import IntegerRing_class
-            sage: IntegerRing_class._cmp_(ZZ,ZZ)
-            0
-            sage: IntegerRing_class._cmp_(ZZ,QQ)
-            -1
-        """
         if isinstance(right, IntegerRing_class):
-            return 0
-        if isinstance(right, sage.rings.rational_field.RationalField):
-            return -1
-        return -1  # arbitrary
+            return rich_to_bool(op, 0)
+
+        return op == Py_NE
 
     def _repr_(self):
         """