Self-distributive operations

Definition

Let $\cdot\colon M \times M\to M$ be a binary operation, i.e. $(M,\cdot)$ is a magma. We say that the operation $\cdot$ is

• left self-distributive if for all $x,y,z\in M$, $x\cdot(y\cdot z) = (x\cdot y)\cdot (x\cdot z)$;
• right self-distributive if for all $x,y,z\in M$, $(y\cdot z)\cdot x = (y\cdot x)\cdot (z\cdot x)$.