Definition:(1-3) Parastrophe

Definition
Let $S$ be a set.

Let $\struct {S, \circ_1}$ and $\struct {S, \circ_2}$ be magmas on $S$.

$\struct {S, \circ_2}$ is a $(1-3)$ parastrophe of $\struct {S, \circ_1}$ :


 * $\forall x_1, x_2, x_3 \in S: x_1 \circ_1 x_2 = x_3 \iff x_3 \circ_2 x_2 = x_1$

Also see

 * Definition:Parastrophe


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