\begin{definition}[Definition:Alternating Bilinear Mapping/Characteristic Not 2]
Let $R$ be a commutative ring.
Let $\struct {A_R, \oplus}$ be an algebra over $R$.
Let $R$ have a characteristic not equal to $2$.
Then $\oplus$ is an '''alternating bilinear mapping''' {{iff}}:
:$\forall a, b \in A_R: a \oplus b = - b \oplus a$
\end{definition}