Definition:Anticommutative/Structure with Two Operations

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Let $\left({S, +, \circ}\right)$ be an algebraic structure.

Suppose every element $x$ in $\left({S, +}\right)$ has an inverse element $-x$.

Then $\circ$ is anticommutative on $S$ with respect to $+$ if and only if:

$\forall x, y \in S: x \circ y = -\left({y \circ x}\right)$

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This article incorporates material from Anticommutative on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.