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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
Affiliation:
Fakultät für MathematikUniversität WienNordbergstrasse 15A-1090 WienAustria e-mail: [email protected]
M. B. Szendrei
Affiliation:
Bolyai InstituteUniversity of SzegedAradi vértanúk tere 1H-6720 SzegedHungary e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

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