diff --git a/MatricesForHomalg/PackageInfo.g b/MatricesForHomalg/PackageInfo.g
index c969ddd34..62b2d88cc 100644
--- a/MatricesForHomalg/PackageInfo.g
+++ b/MatricesForHomalg/PackageInfo.g
@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "MatricesForHomalg",
 Subtitle := "Matrices for the homalg project",
-Version := "2024.08-04",
+Version := "2024.08-05",
 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 08646b72a..9d03da160 100644
--- a/MatricesForHomalg/gap/Tools.gi
+++ b/MatricesForHomalg/gap/Tools.gi
@@ -8015,7 +8015,7 @@ InstallMethod( RingMapOntoRewrittenResidueClassRing,
     fi;
     
     ## R = A / I
-    I := MatrixOfRelations( R );
+    I := BasisOfRows( MatrixOfRelations( R ) );
     
     A := AmbientRing( R );
     
@@ -8047,7 +8047,9 @@ InstallMethod( RingMapOntoRewrittenResidueClassRing,
     zero_rows := ZeroRows( matrix - images );
     
     ## create the standard subring S of A, i.e., the subring generated by the standard indeterminates
-    if Length( indets ) = Length( zero_rows ) and
+    if IsZero( DecideZeroRows( HomalgIdentityMatrix( 1, A ), I ) ) then
+        S := k / One( k );
+    elif Length( indets ) = Length( zero_rows ) and
        IsIdenticalObj( k, CoefficientsRing( A ) ) then
         S := A;
     else
@@ -8091,8 +8093,22 @@ InstallMethod( RingMapOntoSimplifiedOnceResidueClassRing,
     fi;
     
     ## R = A / I
+    A := AmbientRing( R );
+    
     I := MatrixOfRelations( R );
     
+    ## [ y_1, ..., y_{i-1}, y_i, y_{i+1}, ..., y_s ]
+    indets := ShallowCopy( Indeterminates( A ) );
+    
+    if IsEmpty( indets ) and IsZero( DecideZeroRows( HomalgIdentityMatrix( 1, A ), I ) ) then
+        S := CoefficientsRing( A ) / 1;
+        SetIsZero( S, true );
+        epi := RingMap( ListWithIdenticalEntries( Length( indets ), Zero( S ) ), A, S );
+        SetIsMorphism( epi, true );
+        SetIsEpimorphism( epi, true );
+        return epi;
+    fi;
+    
     for i in [ 1 .. NumberRows( I ) ] do
         ## [ j, f/u ] where (u y_j - f) ∈ GB(I)
         img := IsolateIndeterminate( I[ i, 1 ] );
@@ -8102,14 +8118,12 @@ InstallMethod( RingMapOntoSimplifiedOnceResidueClassRing,
     od;
     
     if img = fail then
-        return id;
+        epi := RingMap( List( indets, a -> a / R ), A, R );
+        SetIsMorphism( epi, true );
+        SetIsEpimorphism( epi, true );
+        return epi;
     fi;
     
-    A := AmbientRing( R );
-    
-    ## [ y_1, ..., y_{i-1}, y_i, y_{i+1}, ..., y_s ]
-    indets := ShallowCopy( Indeterminates( A ) );
-    
     new_indets := List( indets, String );
     
     ## [ y_1, ..., y_{i-1}, y_{i+1}, ..., y_s ]
@@ -8159,7 +8173,8 @@ InstallMethod( RingMapOntoSimplifiedResidueClassRing,
         ## construct the surjective morphism psi: A_i -> A_{i+1} / I_{i+1} =: R_{i+1}
         psi := RingMapOntoSimplifiedOnceResidueClassRing( Range( pi ) );
         
-        if HasIsOne( psi ) and IsOne( psi ) then
+        if ( HasIsZero( Range( psi ) ) and IsZero( Range( psi ) ) ) or
+           Length( Indeterminates( Source( psi ) ) ) = Length( Indeterminates( Range( psi ) ) ) then
             break;
         fi;
         
@@ -8254,7 +8269,8 @@ InstallMethod( RingMapOntoSimplifiedResidueClassRingUsingLinearEquations,
         ## 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 ) ) or ( HasIsZero( Range( psi ) ) and IsZero( Range( psi ) ) ) then
+        if ( HasIsZero( Range( psi ) ) and IsZero( Range( psi ) ) ) or
+           Length( Indeterminates( Source( psi ) ) ) = Length( Indeterminates( Range( psi ) ) ) then
             break;
         fi;