Nil element

This article defines a property of elements or tuples of elements with respect to a binary operation

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. For full proof, refer: Equality of left and right nil element