Left nuclear square magma

Symbol-free definition
A magma is termed a left nuclear square magma if every defining ingredient::square element of the magma is inside the defining ingredient::left nucleus.

Definition with symbols
A magma $$(S,*)$$ is termed a left nuclear square magma if the following identity is satisfied for all $$x,y,z \in S$$:

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

An algebra loop that is also a left nuclear square magma is termed a left nuclear square loop.