Abundant semigroups with medial idempotents

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{item۶} will be revisited.

کلیدواژه ها:

Abundant semigroups ، Ample semigroups ، Medial idempotents ، Naturally ordered semigroups