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 chain e 0 > e 1 > e 2 .… 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.