Definition:Opposite Magma

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Definition

Let $\left({S, \circ}\right)$ and $\left({S, *}\right)$ be magmas.


Then $\left({S, *}\right)$ is the opposite magma of $\left({S, \circ}\right)$ if and only if:

$\forall x, y, z \in S: x \circ y = z \iff y * x = z$


The operation $*$ is sometimes referred to as the opposite law of $\circ$.


Also known as

This concept was introduced with this name in the books by Nicolas Bourbaki.

Other sources refer to $\left({S, *}\right)$, as defined here, as the ($1$-$2$) parastrophe of $\left({S, \circ}\right)$.


Also see