\begin{definition}[Definition:R-Balanced Mapping]
Let $R$ be a ring.
Let $M$ be a right $R$-module and $N$ be a left $R$-module.
Let $M \times N$ be their cartesian product.
Let $P$ be an abelian group.
An '''$R$-balanced mapping''' $f : M \times N \to P$ is a biadditive mapping with:
:$\forall m \in M: \forall n \in N: \forall r \in R: \map f {m \cdot r, n} = \map f {m, r \cdot n}$
\end{definition}