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On the lattice of varieties of completely regular semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. R. Jones
P. R. Jones
Affiliation:
Department of Mathematics, Statistics and Computer Science Marquette UniversityMilwaukee, Wisconsin 53233, U.S.A.
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Abstract

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Several morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 227 - 235
Copyright
Copyright © Australian Mathematical Society 1983

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