INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS

Singha, Boorapa; Sanwong, Jintana; Sullivan, Robert Patrick

doi:10.4134/BKMS.2012.49.1.109

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INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS

Journal title : Bulletin of the Korean Mathematical Society
Volume 49, Issue 1, 2012, pp.109-126
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2012.49.1.109

Title & Authors

INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
Singha, Boorapa; Sanwong, Jintana; Sullivan, Robert Patrick;

Abstract

In 2003, Marques-Smith and Sullivan described the join ${${\Omega}$}$ of the 'natural order' ${$\leq$}$ and the 'containment order' ${$\subseteq$}$ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective ${${\alpha}{\in}P(X)$}$ such that ${${\mid}X{\backslash}X{\alpha}\mid=q$}$ , where ${$N_0{\leq}q{\leq}{\mid}X{\mid}$}$ . In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of ${$\leq$}$ and ${$\subseteq$}$ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since ${$\leq$}$ does not equal ${${\Omega}$}$ on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of ${${\Omega}$}$ on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting.

Keywords

partial transformation semigroup;Baer-Levi semigroup;inverse semigroup;natural order;containment order;meet and join;

Language

English

Cited by

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