Let 0-->M-->V-->W-->0 be an exact sequence of algebra's. We can then see that W = V/M. (is this true? Wouldn't W = V/Im(M)?) Then i wrote 'codimension 1 in a nilpotent algebra,' no idea why i wrote it. Anyone, if V is a nilpotent algebra, then V^2 < V. Let M be a comdension 1 subspace of V containing V^2, then M is an ideal. (Why is this?) The algebra structure of W is trivial. (Why is this?) If anyone can shed some light on any of this it would be much appreciated.