Definition:Bilinear Mapping/Non-Commutative Ring

Definition
Let $R$ and $S$ be rings.

Let $M$ be a right $R$-module.

Let $N$ be a left $S$-module.

Let $T$ be an $\tuple {R, S}$-bimodule.

A bilinear mapping $f: M \times N \to T$ is a mapping which satisfies:

Also see

 * Definition:Bilinear Form