International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 357816, 5 pages
doi:10.1155/2010/357816
Research Article

On Maximal Ideals of Compact Connected Topological Semigroups

Phoebe McLaughlin,1 Shing S. So,1 and Haohao Wang2

1Department of Mathematics and Computer Science, University of Central Missouri, Warrensburg, MO 64093, USA
2Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, USA

Received 24 May 2010; Accepted 27 August 2010

Academic Editor: Harvinder S. Sidhu

Copyright © 2010 Phoebe McLaughlin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Several results concerning ideals of a compact topological semigroup S with S2=S can be found in the literature. In this paper, we further investigate in a compact connected topological semigroup S how the conditions S2=S and S2≠S affect the structure of ideals of S, especially the maximal ideals.