diff --git a/GaussForHomalg/PackageInfo.g b/GaussForHomalg/PackageInfo.g
index e221143e1..8245935cc 100644
--- a/GaussForHomalg/PackageInfo.g
+++ b/GaussForHomalg/PackageInfo.g
@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "GaussForHomalg",
 Subtitle := "Gauss functionality for the homalg project",
-Version := "2024.07-01",
+Version := "2024.08-01",
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
 
diff --git a/GaussForHomalg/gap/GaussTools.gi b/GaussForHomalg/gap/GaussTools.gi
index d30dd2374..57ee700e7 100644
--- a/GaussForHomalg/gap/GaussTools.gi
+++ b/GaussForHomalg/gap/GaussTools.gi
@@ -397,7 +397,7 @@ InstallValue( CommonHomalgTableForGaussTools,
 
 InstallGlobalFunction( HOMALG_RING_OF_INTEGERS_PRIME_POWER_HELPER,
   function( argument_list, c )
-    local nargs, d, R;
+    local nargs, d, F, R;
     nargs := Length( argument_list );
     if IsPrime( c ) then
         if nargs > 1 and IsPosInt( argument_list[2] ) then
@@ -405,12 +405,14 @@ InstallGlobalFunction( HOMALG_RING_OF_INTEGERS_PRIME_POWER_HELPER,
         else
             d := 1;
         fi;
-        R := CreateHomalgRing( GF( c, d ) );
+        F := GF( c, d );
+        R := CreateHomalgRing( F );
         
         SetRingFilter( R, IsHomalgRing );
         SetRingElementFilter( R, IsFFE );
         
         R!.NameOfPrimitiveElement := Concatenation( "Z", String( c ), "_", String( d ) );
+        SetPrimitiveElement( R, PrimitiveElement( F ) / R );
         SetIsFieldForHomalg( R, true );
         SetRingProperties( R, c, d );
     else
diff --git a/MatricesForHomalg/PackageInfo.g b/MatricesForHomalg/PackageInfo.g
index cb8bd7bf8..dcd2fb69f 100644
--- a/MatricesForHomalg/PackageInfo.g
+++ b/MatricesForHomalg/PackageInfo.g
@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "MatricesForHomalg",
 Subtitle := "Matrices for the homalg project",
-Version := "2024.07-01",
+Version := "2024.08-01",
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
 
diff --git a/MatricesForHomalg/gap/HomalgRing.gd b/MatricesForHomalg/gap/HomalgRing.gd
index 9eee023d2..6a5bdadad 100644
--- a/MatricesForHomalg/gap/HomalgRing.gd
+++ b/MatricesForHomalg/gap/HomalgRing.gd
@@ -1604,6 +1604,19 @@ DeclareAttribute( "AssociatedGradedRing",
 DeclareAttribute( "AssociatedPolynomialRing",
         IsHomalgRing );
 
+##  <#GAPDoc Label="PrimitiveElement">
+##  <ManSection>
+##    <Attr Arg="R" Name="PrimitiveElement"/>
+##    <Returns>a homalg ring element</Returns>
+##    <Description>
+##      The primitive element of the &homalg; field <A>R</A>.
+##   </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "PrimitiveElement",
+        IsHomalgRing );
+
 ####################################
 #
 # global functions and operations:
diff --git a/MatricesForHomalg/gap/HomalgRing.gi b/MatricesForHomalg/gap/HomalgRing.gi
index 3526f0eb3..362b7af2b 100644
--- a/MatricesForHomalg/gap/HomalgRing.gi
+++ b/MatricesForHomalg/gap/HomalgRing.gi
@@ -413,6 +413,21 @@ InstallMethod( BaseRing,
         
   CoefficientsRing );
 
+##
+InstallMethod( PrimitiveElement,
+        "for homalg fields",
+        [ IsFieldForHomalg ],
+        
+  function( R )
+    
+    if not IsBound( R!.NameOfPrimitiveElement ) then
+        TryNextMethod( );
+    fi;
+    
+    return R!.NameOfPrimitiveElement / R;
+    
+end );
+
 ####################################
 #
 # methods for operations: