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Saturated and epimorphically closed varieties of semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. M. Higgins
P. M. Higgins
Affiliation:
Department of Mathematics Monash University Clayton, Victoria 3168, Australia
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Abstract

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We establish a necessary condition (E) for a semigroup variety to be closed under the taking of epimorphisms and a necessary condition (S) for a variety to consist entirely of saturated semigroups. Condition (S) is shown to be sufficient for heterotypical varieties and a stronger condition (S′) is shown to be sufficient for homotypical varieties.

Keywords

semigroupvarietyepimorphismdiminionsaturatedhomotypicalheterotypical

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 20M05: Free semigroups, generators and relations, word problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 2 , April 1984 , pp. 153 - 175
Copyright
Copyright © Australian Mathematical Society 1984

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