Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups

Abstract

Abstract A partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that { } has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.