Abundant semigroups with medial idempotents
Abdulsalam El-Qallali · Categories and General Algebraic Structures with Application · 2021
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.