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Expansions of inverse semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mark V. Lawson ,
Stuart W. Margolis  and
Benjamin Steinberg
Mark V. Lawson
Affiliation:
Division of Mathematics, School of Informatics, University of Wales, Gwynedd LL57 1UT, Wales, e-mail: m.v.lawson@bangor.ac.uk
Stuart W. Margolis
Affiliation:
Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel, e-mail: margolis@macs.biu.ac.il
Benjamin Steinberg
Affiliation:
Department of Pure Mathematics, Faculty of Science, University of Porto, 4099-002 Porto, Portugal
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Abstract

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We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we term F-morphisms. These play the same role in the theory of idempotent-pure homomorphisms that F-inverse monoids play in the theory of E-unitary inverse semigroups.

Keywords

Inverse semigroupsexpansionsF-inverse semigroupsprehomomorphismsBirget-Rhodes expansion.

MSC classification

Secondary: 20M18: Inverse semigroups 20M17: Regular semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 2 , April 2006 , pp. 205 - 228
Copyright
Copyright © Australian Mathematical Society 2006

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