International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 489674, 14 pages
http://dx.doi.org/10.1155/2011/489674

Research Article

On Maximal Subsemigroups of Partial Baer-Levi Semigroups

Boorapa Singha¹ and Jintana Sanwong^1,2

¹Department of Mathematics, Chiang Mai University, Chiangmai 50200, Thailand
²Material Science Research Center, Faculty of Science, Chiang Mai University, Chiangmai 50200, Thailand

Received 20 September 2010; Revised 14 January 2011; Accepted 28 February 2011

Academic Editor: Robert Redfield

Copyright © 2011 Boorapa Singha and Jintana Sanwong. 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

Suppose that is an infinite set with and is the symmetric inverse semigroup defined on . In 1984, Levi and Wood determined a class of maximal subsemigroups (using certain subsets of ) of the Baer-Levi semigroup dom and . Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of , but these are far more complicated to describe. It is known that is a subsemigroup of the partial Baer-Levi semigroup . In this paper, we characterize all maximal subsemigroups of when , and we extend to obtain maximal subsemigroups of when .