diff --git a/MatricesForHomalg/PackageInfo.g b/MatricesForHomalg/PackageInfo.g
index bc60b8234..9fe7ba03f 100644
--- a/MatricesForHomalg/PackageInfo.g
+++ b/MatricesForHomalg/PackageInfo.g
@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "MatricesForHomalg",
 Subtitle := "Matrices for the homalg project",
-Version := "2024.06-04",
+Version := "2024.06-05",
 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/Tools.gi b/MatricesForHomalg/gap/Tools.gi
index d4956b6c2..1667e9700 100644
--- a/MatricesForHomalg/gap/Tools.gi
+++ b/MatricesForHomalg/gap/Tools.gi
@@ -8187,6 +8187,8 @@ InstallMethod( RingMapOntoSimplifiedOnceResidueClassRingUsingLinearEquations,
     
     if not HasAmbientRing( R ) then
         return id;
+    elif HasIsZero( R ) and IsZero( R ) then
+        return id;
     fi;
     
     ## R = A / I
@@ -8228,3 +8230,42 @@ InstallMethod( RingMapOntoSimplifiedOnceResidueClassRingUsingLinearEquations,
     return epi;
     
 end );
+
+##
+InstallMethod( RingMapOntoSimplifiedResidueClassRingUsingLinearEquations,
+        "for a homalg ring",
+        [ IsHomalgRing ],
+        
+  function( R )
+    local id, pi, psi;
+    
+    id := RingMap( R );
+    
+    if not HasAmbientRing( R ) then
+        return id;
+    fi;
+    
+    # R = A / I
+    pi := RingMap( Indeterminates( R ), AmbientRing( R ), R );
+    
+    SetIsMorphism( pi, true );
+    SetIsEpimorphism( pi, true );
+    
+    while true do
+        
+        ## construct the surjective morphism psi: A_i -> A_{i+1} / I_{i+1} =: R_{i+1}
+        psi := RingMapOntoSimplifiedOnceResidueClassRingUsingLinearEquations( Range( pi ) );
+        
+        if HasIsOne( psi ) and IsOne( psi ) then
+            break;
+        fi;
+        
+        ## compose A -pi-> A_i / I_i -psi-> A_{i+1} / I_{i+1},
+        ## where we understand the above psi as the isomorphism psi: A_i / I_i -psi-> A_{i+1} / I_{i+1}
+        pi := PreCompose( pi, psi );
+        
+    od;
+    
+    return pi;
+    
+end );