Abundant Semigroups With Medial Idempotents

Document Type: Research Paper

Author

Department of Mathematics, Faculty of Science, University of Tripoli, Tripoli, Libya

Abstract

The effect of the existence of a medial or related idempotent in any abundant semigroup is the subject of this paper. The aim is to naturally order any abundant semigroup $S$ which contains an ample multiplicative medial idempotent $u$ in a way that $\mathcal{L}^*$ and $\mathcal{R}^*$ are compatible  with the natural order and $u$ is a maximum idempotent. The structure of an abundant semigroup containing an ample normal medial idempotent studied in \cite{item6} will be revisited.

Keywords


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