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Mal'cev products 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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Whilst the Mal'cev product of completely regular varieties need not again be a variety, it is shown that in many important instances a variety is in fact obtained. However, unlike the product of group varieties this product is nonassociative.

Two important operators introduced by Reilly are studied in the context of Mal'cev products. These operators are shown to generate from any given variety one of the networks discovered by Pastijn and Trotter, enabling identities to be provided for the varieties in the network. In particular the join O V BG of the varieties of orthogroups and of bands of groups is determined, answering a question of Petrich.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 227 - 246
Copyright
Copyright © Australian Mathematical Society 1987

References

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