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REES MATRIX COVERS FOR A CLASS OF SEMIGROUPS WITH LOCALLY COMMUTING IDEMPOTENTS

Published online by Cambridge University Press:  20 January 2009

Tanveer A. Khan  and
Mark V. Lawson
Tanveer A. Khan
Affiliation:
School of Mathematics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL57 1UT, UK
Mark V. Lawson
Affiliation:
School of Mathematics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL57 1UT, UK
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Abstract

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McAlister proved that every regular locally inverse semigroup can be covered by a regular Rees matrix semigroup over an inverse semigroup by means of a homomorphism which is locally an isomorphism. We generalize this result to the class of semigroups with local units whose local submonoids have commuting idempotents and possessing what we term a ‘McAlister sandwich function’.

AMS 2000 Mathematics subject classification: Primary 20M10. Secondary 20M17

Keywords

Rees matrix coverslocally inverse semigroupssemigroups with local unitssemigroups with commuting idempotents
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 173 - 186
Copyright
Copyright © Edinburgh Mathematical Society 2001