Right-alternative magma

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

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

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