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Associativity of the regular semidirect product of existence varieties

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Bernd Billhardt  and
Mária B. Szendrei
Bernd Billhardt
Affiliation:
Universität-Gesamthochschule KasselFachbereich 17 Mathematik/Informatik D–34109 Kassel Holländische Str. 36Germany e-mail: [email protected]
Mária B. Szendrei
Affiliation:
University of Szeged Bolyai InstituteH–6720 Szeged Aradi vértanúk tere 1Hungary e-mail: [email protected]
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Abstract

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The associativity of the regular semidirect product of existence varieties introduced by Jones and Trotter was proved under certain condition by Reilly and Zhang. Here we estabilsh associativity in many new cases. Moreover, we prove that the regular semidirect product is right distributive with respect to the join operation. In particular, both associativity and right distriutivity yiel within the varieties of completely simple semigroups. Analogous results are obtainedj for e-pseudovarieties of finite regular semigroups.

MSC classification

Secondary: 20M17: Regular semigroups 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 85 - 115
Copyright
Copyright © Australian Mathematical Society 2000

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