\begin{definition}[Definition:Anticommutative/Structure with Two Operations]
Let $\struct {S, +, \circ}$ be an algebraic structure.
Let every element $x$ in $\struct {S, +}$ have an inverse element $-x$.
Then $\circ$ is '''anticommutative on $S$ with respect to $+$''' {{iff}}:
:$\forall x, y \in S: x \circ y = -\paren {y \circ x}$
\end{definition}