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
M. B. Szendrei
  Bolyai Institute
  University of Szeged
  Aradi vértanúk tere 1
  H-6720 Szeged

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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