Let A be an algebra over some field (e.g., Rationals) and L := LeftIdeal(A, [g]); be a left ideal generated by some element g. It seems that it is impossoble to consider the quotinet module A/L of A. Hence, I consider the left regular module of A, i.e., A considered as a left module over itself. GAP provides F:=AdjointModule(A). For some g in F I issue I:=SubAlgebraModule(A, [g]); and pass to the quotient pi:=NaturalHomomorphismBySubAlgebraModule(F,L); Q:=Range(pi);. Now, assume q in Q. I can find a m:=PreImagesRepresentative(pi, q); of q in F. But actually, this is an element of A, which GAP sees different:
> m in F;
true
> m in A;
false
so how can I take an element of the left regular module F and obtain the corresponding element of A?