Definition:(1-3) Parastrophe

Definition

Let $S$ be a set.

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

$\struct {S, *}$ is a $(1-3)$ parastrophe of $\struct {S, \circ}$ if and only if:

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

Also see

• Definition:Parastrophe

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

• Results about parastrophes can be found here.

Sources

• 2015: W.A. Dudek: Parastrophes of Quasigroups (Quasigroups and Related Systems Vol. 23: pp. 221 – 230)