Jordan magma

Definition
A magma $$(S,*)$$ is termed a Jordan magma if it satisfies the following two conditions:


 * 1) Commutativity: $$\! x * y = y * x \ \forall \ x,y \in S$$.
 * 2) Jordan's identity: $$\! (x * y) * (x * x) = x * (y * (x * x)) \ \forall x,y \in S$$.