J. Aust. Math. Soc.
80 (2006), 205228

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




Benjamin Steinberg
Department of Pure Mathematics
Faculty of Sciences
University of Porto
4099002 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 idempotentpure
expansion of an inverse semigroup, generalizing
an expansion of Margolis and Meakin for the group
case. We also generalize the BirgetRhodes
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
idempotentpure homomorphisms which we term
Fmorphisms. These play the same role in the
theory of idempotentpure homomorphisms that
Finverse monoids play in the theory of
Eunitary inverse semigroups.

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