Definition:Zero Complement

Definition
Let $\left({S, \circ, \preceq}\right)$ be a naturally ordered semigroup.

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

Let $S^* := \complement_S \left({\left\{{0}\right\}}\right)$ be the complement of $\left\{{0}\right\}$ in $S$.

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

Also see

 * Zero Complement is not Empty