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The lattice of completely regular semigroup varieties

Part of: Varieties Semigroups

Published online by Cambridge University Press:  09 April 2009

Francis Pastijn
Francis Pastijn
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53233, U.S.A.
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Abstract

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A completely regular semigroup is a semigroup which is a union of groups. The class CR of completely regular semigroups forms a variety. On the lattice L (CR) of completely regular semigroup varieties we define two closure operations which induce complete congruences. The consideration of a third complete congruence on L (CR) yields a subdirect decomposition of L (CR). Using these results we show that L (CR) is arguesian. This confirms the (tacit) conjecture that L (CR) is modular.

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20M07: Varieties and pseudovarieties of semigroups 08B15: Lattices of varieties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 24 - 42
Copyright
Copyright © Australian Mathematical Society 1990

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