\begin{definition}[Definition:Biadditive Mapping]
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:
:$\forall m_1, m_2 \in M : \forall n \in N: \map f {m_1 + m_2, n} = \map f {m_1, n} + \map f {m_2, n}$
:$\forall m \in M: \forall n_1, n_2 \in N: \map f {m, n_1 + n_2} = \map f {m, n_1} + \map f {m, n_2}$
\end{definition}