Bisimple ω-Semigroups

Abstract

The structure of a bisimple inverse semigroup with an identity has been related by Clifford [2] to that of its right unit subsemigroup. In this paper we give an explicit structure theorem for bisimple inverse semigroups in which the idempotents form a simple descending chaine0 > e1 > e2.…We call such a semigroup a bisimple co-semigroup. The structure of a semigroup of this kind is shown to be determined entirely by its group of units and an endomorphism of its group of units.