On maximal subsemigroups of partial Baer-Levi semigroups

Abstract

Suppose that X is an infinite set with | X | ≥ q ≥ ℘0and I (X) is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA(using certain subsets A of X) of the Baer-Levi semigroup B L (q) = {α ∈ I (X): dom α = X and | X\Xα | = q }. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of B L (q), but these are far more complicated to describe. It is known that B L (q) is a subsemigroup of the partial Baer-Levi semigroup PS(q)={α ∈ I(X):| X\X α | = q }. In this paper, we characterize all maximal subsemigroups of P S (q) when | X | > q, and we extend MAto obtain maximal subsemigroups of P S (q) when | X | = q. Copyright © 2011 Boorapa Singha and Jintana Sanwong.