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INJECTIVE TRANSFORMATIONS WITH EQUAL GAP AND DEFECT

Part of: Semigroups

Published online by Cambridge University Press:  13 March 2009

JINTANA SANWONG  and
R. P. SULLIVAN
JINTANA SANWONG
Affiliation:
Department of Mathematics, Chiangmai University, Chiangmai, 50200, Thailand
R. P. SULLIVAN*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands 6009, Australia (email: bob@maths.uwa.edu.au)
*
✉For correspondence; e-mail: bob@maths.uwa.edu.au
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Abstract

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Suppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α∈I(X), we let dom α and ran α denote the domain and range of α, respectively, and we say that g(α)=|X/dom α| and d(α)=|X/ran α| is the ‘gap’ and the ‘defect’ of α, respectively. In this paper, we study algebraic properties of the semigroup . For example, we describe Green’s relations and ideals in A(X), and determine all maximal subsemigroups of A(X) when X is uncountable.

Keywords

factorizable inverse semigroupgapdefectGreen’s relationsidealsmaximal subsemigroup

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 327 - 336
Copyright
Copyright © Australian Mathematical Society 2009

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