On the construction of a class of regular semigroups

Abstract

In a previous publication [1] we gave a complete description of the internal structure of naturally ordered regular semigroups that have a greatest idempotent, and on which Green's relations R and L are regular. In this paper we describe a method of constructing all such semigroups. The purely algebraic basis of this is the construction of all regular semigroups S that possess a medial idempotent u (i.e., an idempotent such that if E is the subsemigroup of S generated by the idempotents, then (∀× ϵ E) x = xux ) which is normal (in the sense that u E ̄ u is a semilattice).