Center of a loop

Definition
Let $$L$$ be an algebra loop with binary operation $$*$$. Then, the center of $$L$$, denoted as $$Z(L)$$, is defined as the set of all elements $$a \in L$$ satisfying:

$$a * (x * y) = x * (a * y) = (x * a) * y = (x * y) * a \forall x,y \in L$$