In this talk I will present our recent results on the algebraic structure of $\omega$-stable bilinear maps, arbitrary rings and nilpotent groups. I will also discuss some rather complete structure theorems for the above structures in the finite Morley rank case. The main technique in this work is associating a canonical scalar (commutative associative unitary) ring to a bilinear map. This canonical scalar ring happens to preserve many of the logical and algebraic properties of the bilinear map. This talk is based on the joint work with Alexei Miasnikov.