diff --git a/lib/ring.gi b/lib/ring.gi
index 4b5b411ad7..ca631d6fe8 100644
--- a/lib/ring.gi
+++ b/lib/ring.gi
@@ -702,7 +702,7 @@ InstallMethod( IsIntegralRing,
         zero := Zero( R );
         for i  in [1..Length(elms)]  do
             if elms[i] = zero then continue; fi;
-            for k  in [i+1..Length(elms)]  do
+            for k  in [i..Length(elms)]  do
                 if elms[k] = zero then continue; fi;
                 if elms[i] * elms[k] = zero then
                     return false;
diff --git a/tst/testinstall/ring.tst b/tst/testinstall/ring.tst
new file mode 100644
index 0000000000..a1beb16362
--- /dev/null
+++ b/tst/testinstall/ring.tst
@@ -0,0 +1,30 @@
+gap> START_TEST("ring.tst");
+
+#####################################################################
+#
+# Tests for IsIntegralRing
+#
+# Trivial ring
+gap> IsIntegralRing( SmallRing(1,1) );
+false
+
+# Non-commutative ring
+gap> IsIntegralRing( SmallRing(4,7) );
+false
+
+# Zero divisors on the diagonal
+gap> IsIntegralRing( SmallRing(4,3) );
+false
+
+# Integral rings
+gap> IsIntegralRing( GF(5) );
+true
+gap> IsIntegralRing( Integers );
+true
+gap> IsIntegralRing( Rationals );
+true
+gap> IsIntegralRing( CF(4) );
+true
+
+#
+gap> STOP_TEST( "ring.tst" );