Definition:Alternating Bilinear Mapping

Definition
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 :
 * $\forall a \in A_R: a \oplus a = 0$

Also see

 * Definition:Alternating Bilinear Form


 * Equivalence of Definitions for Alternating Bilinear Mapping on Ring of Characteristic Not 2