Bugfix and test for IsIntegralRing

This fixes an off-by-one error causing missing the case
when zero appears in the diagonal in the multiplication table.

Closes gap-system#3975.

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;

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" );