\begin{definition}[Definition:Alternating Bilinear Mapping]
Let $R$ be a commutative ring.
Let $\struct {A_R, \oplus}$ be an algebra over $R$.
By definition, $\oplus$ is a bilinear mapping.
Then $\oplus$ is an '''alternating bilinear mapping''' {{iff}}:
:$\forall a \in A_R: a \oplus a = 0$
\end{definition}