# Definition:Zero Complement

## Definition

Let $\struct {S, \circ, \preceq}$ be a naturally ordered semigroup.

Let $0$ be the zero of $S$.

Let $S^* := \relcomp S {\set 0} = S \setminus \set 0$ be the complement of $\set 0$ in $S$.

Then $S^*$ is called the zero complement of $S$.