Some Classes Of Semigroups That Have Medial Idempotent And Some Construction Theorem

Abstract

It's known that the set of idempotents of the semigroup, plays an important role forthe structure of this semigroup. Specially, in the regular semigroups, an importantrole plays presence of the medial idempotent and normal medial idempotent.Blyth,T. S and R. B. McFadden have studied and constructed the regular semi groups which contain a normal medial idempotent in terms of idempotent-generated regular semi groups with a normal medial idempotent and inverse semigroups with anidentity. M.Loganathan has described the construction of the regular semigroupswhich contain a medial idempotent. In this paper we will study further properties of medial idempotents on abundant semigroups. We will apply also the constructiontheory of abundant semigroups with a medial idempotent to quasi-adequate semigroups and will make a description of structure of those subsemigroups.