Coercions to the fraction field are injective

sagemath · Oct 5, 2017 · 55b33e4 · 55b33e4
1 parent cc613b1
commit 55b33e4
Showing 1 changed file with 10 additions and 0 deletions.
diff --git a/src/sage/categories/rings.py b/src/sage/categories/rings.py
@@ -128,6 +128,12 @@ def is_injective(self):
                 sage: f.is_injective()
                 True
 
+            A coercion to the fraction field is injective::
+
+                sage: R = ZpFM(3)
+                sage: R.fraction_field().coerce_map_from(R).is_injective()
+                True
+
             """
             if self.domain().is_zero():
                 return True
@@ -155,6 +161,10 @@ def is_injective(self):
                         if self.domain().fraction_field() in NumberFields():
                             return True
 
+            if self._is_coercion:
+                if self.domain().fraction_field() is self.codomain():
+                    return True
+
             if self.domain().cardinality() > self.codomain().cardinality():
                 return False