\begin{definition}[Definition:Bilinear Form]
Let $R$ be a ring.
Let $R_R$ denote the $R$-module $R$.
Let $M_R$ be an $R$-module.
A '''bilinear form''' on $M_R$ is a bilinear mapping $B : M_R \times M_R \to R_R$.
\end{definition}