Definition:Anticommutative/Structure with Two Operations

From ProofWiki
Jump to navigation Jump to search

Definition

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:

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


Also see


Sources