Left Bol magma with neutral element

Definition
A left Bol magma with neutral element is a defining ingredient::left Bol magma that has a defining ingredient::neutral element. In other words, it is a magma $$(S,*)$$ such that:


 * 1) For all $$x,y,z \in S$$, we have $$\! x * (y * (x * z)) = (x * (y * x)) * z$$.
 * 2) There exists $$e \in S$$, we have $$\! x * e = e * x = x$$.