Inverse Semigroups with a Compatible Semilattice Ordering
by
Donald B. McAlister
Northern Illinois University, DeKalb, USA

Inverse semigroups come equipped with a natural partial order which plays a crucial role in the structure theory of these semigroups. Indeed, as Jonathan Leech has pointed out (``Inverse monoids with a natural semilattice ordering'', Proc. London Math Soc. (3)70(1995), 146-182), in most examples of inverse semigroups S of partial symmetries the natural partial ordering is a /\ -semilattice ordering on S. Further, multiplication distributes over /\ so that S becomes a /\ -semilattice ordered inverse semigroup. In this talk I will review some results on the results on the structure of semilattice ordered inverse semigroups in the case when the imposed partial ordering need not agree with the natural partial order on the idempotents. Among topics to be discussed are classical results of Saitô and Bosbach as well as more recent results of Giraldes, Gomes, and the speaker.

Date received: April 6, 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-08.