Category:Definitions/Alternating Bilinear Mappings

This category contains definitions related to Alternating Bilinear Mappings.
Related results can be found in Category:Alternating Bilinear Mappings.

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 if and only if:

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