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PSEUDOVARIETIES, REGULAR SEMIGROUPS AND SEMIDIRECT PRODUCTS

Published online by Cambridge University Press:  01 October 1998

K. AUINGER  and
P. G. TROTTER
K. AUINGER
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
P. G. TROTTER
Affiliation:
Department of Mathematics, University of Tasmania, Hobart 7001, Tasmania, Australia
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Abstract

We compare the classical semidirect product V[midast ] W of pseudovarieties of semigroups with the recently found ‘regular’ semidirect product [Vscr ] [midast ]e [Wscr ] of e-pseudovarieties of regular semigroups. Applications of our findings include a substantial class of additions to the list of pseudovarieties generated by classes of regular semigroups and for which the membership problem is solved. For example, we compute the pseudovarieties generated by all locally inverse and locally orthodox semigroups, respectively, thereby answering a question raised by Almeida and Kaďourek.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 284 - 296
Copyright
The London Mathematical Society 1998

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