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Varieties of completely regular semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Norman R. Reilly
Norman R. Reilly
Affiliation:
Deparment of Mathematics and Statistics, Simon Fraser UniversityBurnaby, B. C. V5A 1A6, Canada
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Abstract

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If CS(respectively, O) denotes the class of all completely simple semigroups (respectively, semigroups that are orthodox unions of groups) then CS(respectively, O) is a variety of algebras with respect to the operations of multiplication and inversion. The main result shows that the lattice of subvarieties of is a precisely determined subdirect product of the lattice of subvarieties of CSand the lattice of subvarieties of O. A basis of identities is obtained for any variety in terms of bases of identities for . Several operators on the lattice of subvarieties of are also introduced and studied.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 3 , June 1985 , pp. 372 - 393
Copyright
Copyright © Australian Mathematical Society 1985

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