Left nuclear square magma

This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.
View other such properties

Definition

A magma is termed a left nuclear square magma if every square element of the magma is inside the left nucleus.

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.