Left alternative magma

Definition
A magma $$(S,*)$$ is termed a left-alternative magma if it satisfies the following identity:

$$x * (x * y) = (x * x) * y \ \forall x,y \in S$$.

Property obtained by the opposite operation
If $$(S,*)$$ is a magma and we define $$\cdot$$ on $$S$$ by $$a \cdot b := b * a$$, then $$(S,*)$$ is a left-alternative magma if and only if $$(S, \cdot)$$ is a right-alternative magma.