Definition:Biadditive Mapping

Definition

Let $M, N, P$ be abelian groups.

Let $M \times N$ be the cartesian product.

A biadditive mapping $f : M \times N \to P$ is a mapping such that:

$\forall m_1, m_2 \in M : \forall n \in N: \map f {m_1 + m_2, n} = \map f {m_1, n} + \map f {m_2, n}$

$\forall m \in M: \forall n_1, n_2 \in N: \map f {m, n_1 + n_2} = \map f {m, n_1} + \map f {m, n_2}$

Also known as

A biadditive mapping is also known as a $\Z$-bilinear mapping. See Correspondence between Abelian Groups and Z-Modules.

Also see

• Definition:Bilinear Mapping

Sources

• 1974: N. Bourbaki: Algebra I: Chapter $\text {II}$. Linear Algebra $\S 3$. Tensor Products. $1$. Tensor product of two modules