diff --git a/src/sage/rings/ring_extension.pyx b/src/sage/rings/ring_extension.pyx
index 2b649359ad4..b493f57bed9 100644
--- a/src/sage/rings/ring_extension.pyx
+++ b/src/sage/rings/ring_extension.pyx
@@ -1885,6 +1885,59 @@ cdef class RingExtension_generic(CommutativeAlgebra):
         parent = self.Hom(codomain, category=category)
         return RingExtensionHomomorphism(parent, im_gens, base_map, check)
 
+    def characteristic(self):
+        r"""
+        Return the characteristic of the extension as a ring.
+
+        OUTPUT:
+
+        A prime number or zero.
+
+        EXAMPLES::
+
+            sage: F = GF(5^2).over()   # over GF(5)
+            sage: K = GF(5^4).over(F)
+            sage: L = GF(5^12).over(K)
+            sage: F.characteristic()
+            5
+            sage: K.characteristic()
+            5
+            sage: L.characteristic()
+            5
+
+        ::
+
+            sage: F = RR.over(ZZ)
+            sage: F.characteristic()
+            0
+
+        ::
+
+            sage: F = GF(11)
+            sage: A.<x> = F[]
+            sage: K = Frac(F).over(F)
+            sage: K.characteristic()
+            11
+
+        ::
+
+            sage: E = GF(7).over(ZZ)
+            sage: E.characteristic()
+            7
+
+        TESTS:
+
+            Ensure ticket :trac:`34692` is fixed::
+
+            sage: Fq = GF(11)
+            sage: FqX.<X> = Fq[]
+            sage: k = Frac(FqX)
+            sage: K = k.over(FqX)
+            sage: K.frobenius_endomorphism()
+            Frobenius endomorphism x |--> x^11 of Fraction Field of Univariate Polynomial Ring in X over Finite Field of size 11 over its base
+        """
+        return self._backend.characteristic()
+
 
 # Fraction fields
 #################