Definition:Opposite Magma

Definition
Let $S$ be a set.

Let $\struct {S, \circ}$ and $\struct {S, *}$ be magmas on $S$.

$\struct {S, *}$ is the opposite magma of $\struct {S, \circ}$ :


 * $\forall x_1, x_2, x_3 \in S: x_1 \circ x_2 = x_3 \iff x_2 * x_1 = x_3$

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.

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

Also see

 * Definition:Parastrophe


 * Definition:(1-3) Parastrophe
 * Definition:(2-3) Parastrophe


 * Opposite Group