diff --git a/hpcgap/lib/ringpoly.gi b/hpcgap/lib/ringpoly.gi
index 64502a72c5..e68c49c3f0 100644
--- a/hpcgap/lib/ringpoly.gi
+++ b/hpcgap/lib/ringpoly.gi
@@ -635,7 +635,7 @@ InstallMethod(StandardAssociateUnit,
 function(R,f)
   local c;
   c:=LeadingCoefficient(f);
-  return StandardAssociateUnit(CoefficientsRing(R),c);
+  return StandardAssociateUnit(CoefficientsRing(R),c) * One(R);
 end);
 
 InstallMethod(FunctionField,"indetlist",true,[IsRing,IsList],
diff --git a/lib/ratfunul.gi b/lib/ratfunul.gi
index 352b6b4cdf..cd4c033922 100644
--- a/lib/ratfunul.gi
+++ b/lib/ratfunul.gi
@@ -1031,7 +1031,7 @@ InstallMethod(StandardAssociateUnit,"laurent",
   IsCollsElms,[IsPolynomialRing, IsLaurentPolynomial],0,
 function(R,f)
   # get standard associate of leading term
-  return StandardAssociateUnit(CoefficientsRing(R), LeadingCoefficient(f));
+  return StandardAssociateUnit(CoefficientsRing(R), LeadingCoefficient(f)) * One(R);
 end);
 
 #############################################################################
diff --git a/lib/ringpoly.gi b/lib/ringpoly.gi
index b973d4f271..92578c7a3e 100644
--- a/lib/ringpoly.gi
+++ b/lib/ringpoly.gi
@@ -633,7 +633,7 @@ InstallMethod(StandardAssociateUnit,
 function(R,f)
   local c;
   c:=LeadingCoefficient(f);
-  return StandardAssociateUnit(CoefficientsRing(R),c);
+  return StandardAssociateUnit(CoefficientsRing(R),c) * One(R);
 end);
 
 InstallMethod(FunctionField,"indetlist",true,[IsRing,IsList],
diff --git a/tst/testinstall/associate.tst b/tst/testinstall/associate.tst
index 59c405f0fc..858a4751ad 100644
--- a/tst/testinstall/associate.tst
+++ b/tst/testinstall/associate.tst
@@ -1,4 +1,4 @@
-#@local checkStandardAssociate
+#@local checkStandardAssociate, A, x, R
 gap> START_TEST("associate.tst");
 
 # test StandardAssociate, StandardAssociateUnit, IsAssociated
@@ -48,5 +48,13 @@ true
 gap> checkStandardAssociate(Integers mod ((2*3*5*7)^3));
 true
 
+# polynomial rings
+gap> for A in [ GF(5), Integers, Rationals ] do
+>      for x in [1,3] do
+>        R:=PolynomialRing(A, x);
+>        checkStandardAssociate(R, List([1..30],i->PseudoRandom(R)));
+>      od;
+>    od;
+
 #
 gap> STOP_TEST("associate.tst", 1);