J. Aust. Math. Soc.  79 (2005), 39-60

Rees matrix semigroups and the regular semidirect product

K. Auinger   Fakultät für Mathematik   Universität Wien   Nordbergstrasse 15   A-1090 Wien   Austria   karl.auinger@univie.ac.at and M. B. Szendrei   Bolyai Institute   University of Szeged   Aradi vértanúk tere 1   H-6720 Szeged   Hungary   m.szendrei@math.u-szeged.hu

Abstract

A generalization of the Pastijn product is introduced so that, on the level of e-varieties and pseudo-e-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.

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