The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups
type: Item
instance of: scholarly article
title: The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups
zbMATH Open document ID: 0845.20047
DOI: 10.1007/BF02574083
author: Peter G. Trotter
author: M. V. Volkov
published in: Semigroup Forum
publication date: 1996-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/135435
review text: Suppose that we take any pseudovariety of finite aperiodic semigroups which includes all finite \(\mathcal J\)-trivial semigroups, and form its join with any non-abelian group pseudovariety. The authors show that the resulting pseudovariety is not finitely based. Using a result of \textit{A. de Azevedo} [Lattices, semigroups and universal algebra, Proc. Int. Conf., Lisbon/Port. 1988, 1-11 (1990; Zbl 0728.08012)], they deduce that the join of a group pseudovariety with the pseudovariety of all finite \(\mathcal J\)-trivial semigroups is finitely based if and only if all the members of the group pseudovariety are abelian. Their methods also shed light on the finite basis problem for the joins of certain semigroup varieties and group varieties.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 20E10
zbMATH DE Number: 836810
zbMATH Keywords: joins of semigroup varieties
zbMATH Keywords: pseudovariety of finite aperiodic semigroups
zbMATH Keywords: finite \(\mathcal J\)-trivial semigroups
zbMATH Keywords: group pseudovariety
zbMATH Keywords: finite basis problem
zbMATH Keywords: group varieties
reviewed by: Graham T. Clarke
MaRDI profile type: Publication
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OpenAlex ID: W2023711663
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description: scientific article; zbMATH DE number 836810