Definition:Alternating Bilinear Mapping
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Definition
Let $\left({A_R, \oplus}\right)$ be an algebra over a ring.
By definition, $\oplus$ is a bilinear mapping.
Then $\oplus$ is an alternating bilinear mapping if and only if:
- $\forall a \in A_R: a \oplus a = 0$
For rings with characteristic other than two, the following condition is equivalent:
- $\forall a, b \in A_R: a \oplus b = - b \oplus a$
Also see