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Operators related to idempotent generated and monoid completely regular semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mario Petrich  and
Norman R. Reilly
Mario Petrich
Affiliation:
Simon Fraser UniversityBurnaby, B.C., Canada
Norman R. Reilly
Affiliation:
Simon Fraser UniversityBurnaby, B.C., Canada
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Abstract

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The class CR of completely regular semigroups (unions of groups or algebras with the associative binary operation of multiplication and the unary operation of inversion subject to the laws x = xx-1, (x−1)-1 = x and xx-1 = x-1x) is a variety. Among the important subclasses of CR are the classes M of monoids and I of idempotent generated members. For each C ∈ {I, M}, there are associated mappings ν → ν ∩ C and ν → (Ν ∩ C), the variety generated by ν ∩ C. The lattice theoretic properties of these mappings and the interactions between these mappings are 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 49 , Issue 1 , August 1990 , pp. 1 - 23
Copyright
Copyright © Australian Mathematical Society 1990

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