On a class of Dubreil-Jacotin regular semigroups and a construction of Yamada

Abstract

SynopsisIn the publication [2] we obtained some structure theorems for certain Dubreil-Jacotin regular semigroups. A crucial observation in the course of investigating these types of ordered regular semigroups was that the (ordered) band of idempotents was normal. This is characteristic of a class of semigroups studied by Yamada [5] and called generalised inverse semigroups. Here we specialise a construction of Yamada to obtain a structure theorem that complements those in [2], The important feature of the present approach is the part played by the greatest elements that exist in each of the components in the semilattice decompositions involved.