Definition:Zero Complement

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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 $S$.


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