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Rees matrix semigroups and the regular semidirect product

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

K. Auinger  and
M. B. Szendrei
K. Auinger
Affiliation:
Fakultät für MathematikUniversität WienNordbergstrasse 15A-1090 WienAustria e-mail: karl.auinger@univie.ac.at
M. B. Szendrei
Affiliation:
Bolyai InstituteUniversity of SzegedAradi vértanúk tere 1H-6720 SzegedHungary e-mail: m.szendrei@math.u-szeged.hu
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Abstract

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A generalization of the Pastijn product is introduced so that, on the level of e-varieties and pseudoe-varieties, this product and the regular semidirect product by completely simple semigroups ‘almost always’ coincide. This is applied to give a model of the bifree objects in every e-variety formed as a regular semidirect product of a variety of inverse semigroups by a variety of completely simple semigroups that is not a group variety.

MSC classification

Secondary: 20M17: Regular semigroups 20M07: Varieties and pseudovarieties of semigroups 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 39 - 60
Copyright
Copyright © Australian Mathematical Society 2005

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