J. Aust. Math. Soc.  80 (2006), 205-228

Expansions of inverse semigroups

Mark V. Lawson   Division of Mathematics   School of Informatics   University of Wales   Gwynedd LL57 1UT   Wales   m.v.lawson@bangor.ac.uk Stuart W. Margolis   Department of Mathematics   Bar Ilan University   52900 Ramat Gan   Israel   margolis@macs.biu.ac.il and Benjamin Steinberg   Department of Pure Mathematics   Faculty of Sciences   University of Porto   4099-002 Porto   Portugal   Current Address:   School of Mathematics and Statistics   Carleton University   1125 Colonel By Drive   Ottawa ON, K1S 5B6   Canada   bsteinbg@math.carleton.ca

Abstract

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.

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