Let be a semigroup. An element is called a right zero [resp. left zero] if [resp. ] for all .

An element which is both a left and a right zero is called a zero element.

A semigroup may have many left zeros or right zeros, but if it has at least one of each, then they are necessarily equal, giving a unique (two-sided) zero element.

It is customary to use the symbol for the zero element of a semigroup.