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VARIETIES GENERATED BY COMPLETELY 0-SIMPLE SEMIGROUPS

Part of: Semigroups Varieties

Published online by Cambridge University Press:  01 June 2008

NORMAN R. REILLY
NORMAN R. REILLY*
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6 (email: nreilly@cs.sfu.ca)
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Abstract

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Kublanovsky has shown that if a subvariety V of the variety RSn generated by completely 0-simple semigroups over groups of exponent n is itself generated by completely 0-simple semigroups, then it must satisfy one of three conditions: (i) A2 ∈ V; (ii) (iii) B2∈V but The conditions (i) and (ii) are also sufficient conditions. In this note, we complete Kublanovsky’s programme by refining condition (iii) to obtain a complete set of conditions that are both necessary and sufficient.

Keywords

semigroupvarietyRees–Sushkevich varietiesexactcompletely 0-simple

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 08B15: Lattices of varieties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 3 , June 2008 , pp. 375 - 403
Copyright
Copyright © 2008 Australian Mathematical Society

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