[GAP Forum] Explicit membership for ideals of group rings

[Xavier Roblot]

Dear all,

I would like to know how to obtain the explicit decomposition of some element of an ideal of a group ring expressed on the generators of this ideal. More precisely, assume that QG is a group ring with G a finite group (in my case, constructed as the quotient of a free group) and that a1, a2 and b are elements of QG. I can do the following:

gap> I = a1*QG + a2*QG;;
gap> b in I;
true

This tells me that b is in the ideal generated by a1 and a2. Is there a way to obtain the explicit decomposition of b in terms of a1 and a2? 

Thanks for your help,

X.-F. Roblot