Given a finite dimensional algebra $A$ and a set of twosided ideals $\{I_1, I_2,...,I_n \}$. Let $G$ be the monoid (or sometimes group) generated by those ideals. Is there a way to obtain this monoid via GAP (or a package like qpa) and check what monoid it is (and wheter it is finite)?
Is there a quick way to get the maximal ideals of the algebra? (at least when its a quiver algebra, this should be easy, but I found no command for that).