On Ordered Completely Simple Semigroups
by
Gonçalo Pinto
Unidade de Investigação em Matemática, Instituto Piaget, Almada, Portugal
Coauthors: T. S. Blyth (Mathematical Institute, University of St. Andrews, Scotland)

In the theory of regular semigroups a significant part is played by those that are completely simple. Compatible orders on such semigroups have been considered. Here we consider those ordered completely simple semigroups that belong to the class of ordered regular semigroups in which every element has a biggest inverse. This class contains, for example, the ordered regular semigroups that are Dubreil-Jacotin, principally ordered and, more particularly, residuated. Our objective is to show that if S=M(G;I;\Lambda;P) is an ordered completely simple semigroup, with G,  I,  \Lambda non-trivial, in which every element has a biggest inverse then S contains one of seven particular types of subsemigroup.

Date received: April 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caec-10.