Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T23:01:41.116Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
John Fountain
Affiliation:
Department of Mathematics Wilfrid Laurier University Waterloo Ontario N2L 3C5 Canada e-mail: [email protected]
Victoria Gould
Affiliation:
Department of Mathematics University of York Heslington York YO10 5DD UK e-mail: [email protected] e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Almeida, J., Pin, J.-E. and Weil, P., ‘Semigroups whose idempotents form a subsemigroup’, Math. Proc. Cambridge Philos. Soc. 111 (1992), 241–253.CrossRefGoogle Scholar
[2]Gomes, G. M. S. and Howie, J. M., ‘A P-theorem for inverse semigroups with zero’, Portugal. Math. 53 (1996), 257–278.Google Scholar
[3]Howie, J. M., Fundamentals of semigroups and theory (Oxford University Press, Oxford, 1995).CrossRefGoogle Scholar
[4]Margolis, S. and Pin, J. E., ‘Inverse semigroups and extensions of groups by semilattices’, J. Algebra 110 (1987), 277–297.CrossRefGoogle Scholar
[5]McAlister, D. B., ‘Groups, semilattices and inverse semigroups’, Trans. Amer. Math. Soc. 192 (1974), 227–244.Google Scholar
[6]McAlister, D. B., ‘Groups, semilattices and inverse semigroups, II’, Trans. Amer. Math. Soc. 196 (1974), 351–370.CrossRefGoogle Scholar
[7]Munn, W. D., ‘Brandt congruences on inverse semigroups’, Proc. London Math. Soc. 14 (1964), 154–164.CrossRefGoogle Scholar
[8]O'Carroll, L., ‘Embedding theorems for proper inverse semigroups’, J. Algebra 42 (1976), 26–40.CrossRefGoogle Scholar
[9]Szendrei, M. B., ‘A generalization of McAlister's P-theorem for E-unitary regular semigroups’, Acta Sci. Math. (Szeged) 51 (1987), 229–249.Google Scholar