Reflexive Unitary Subsemigroups of Left Simple Semigroups

Abstract

Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So it is a natural idea that we try to use the group theoretical methods (instead of the ring theoretical ones) for the examination of these semigroups. The purpose of this paper is to find a suitable type of subsemigroups of left simple semigroups which makes possible for us to generalize some notions (the notion of the normal series and the composition series of groups) and some results concerning the groups to the left simple semigroups. We note that the subsemigroups we are looking for are the reflexive unitary subsemigroups of left simple semigroups.