Nil element

Definition
An element $$n$$ in a magma $$(S,*)$$ is termed a:


 * left nil element if $$n * a = n$$ for all $$a \in S$$.
 * right nil element if $$a * n = n$$ for all $$a \in S$$.
 * nil element if it is both a left nil element and a right nil element.

If both a left nil and a right nil exist, they are equal.