Definition:R-Balanced Mapping
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Definition
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:
- $\forall m \in M: \forall n \in N: \forall r \in R: \map f {m \cdot r, n} = \map f {m, r \cdot n}$