Left Bol magma

Definition
A magma $$(S,*)$$ is termed a left Bol magma if it satisfies the following identity for all $$x,y,z \in S$$:

$$\! x * (y * (x * z)) = (x * (y * x)) * z$$

Typically, the left Bol identity is studied in the context of algebra loops. Such loops are termed left Bol loops. However, some of the properties studied for left Bol loops generalize to left Bol magmas with neutral element.

Stronger properties

 * Weaker than::Left Bol magma with neutral element