# 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 if and only if:

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

### Characteristic Not $2$

Let $R$ have a characteristic not equal to $2$.

Then $\oplus$ is an alternating bilinear mapping if and only if:

$\forall a, b \in A_R: a \oplus b = - b \oplus a$

## Also see

• Results about alternating bilinear mappings can be found here.