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Inverse semigroups with zero: covers and their structure

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Sydney Bulman-Fleming ,
John Fountain  and
Victoria Gould
Sydney Bulman-Fleming
Affiliation:
Department of Mathematics Wilfrid Laurier University Waterloo Ontario N2L 3C5 Canada e-mail: sbulman@mach1.wlu.ca
John Fountain
Affiliation:
Department of Mathematics Wilfrid Laurier University Waterloo Ontario N2L 3C5 Canada e-mail: sbulman@mach1.wlu.ca
Victoria Gould
Affiliation:
Department of Mathematics University of York Heslington York YO10 5DD UK e-mail: jbf1@york.ac.uk e-mail: varg1@york.ac.uk
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Abstract

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We obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroups is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical E*-unitary semigroups recently considered by Gomes and Howie.

Keywords

P-theoremE*-unitarycover.

MSC classification

Secondary: 20M18: Inverse semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 1 , August 1999 , pp. 15 - 30
Copyright
Copyright © Australian Mathematical Society 1999

References

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