Equational theories of semigroups with involution.
type: Item
instance of: scholarly article
title: Equational theories of semigroups with involution.
zbMATH Open document ID: 1294.20072
author: K. Auinger
author: Igor Dolinka
author: M. V. Volkov
published in: Journal of Algebra
publication date: 2013-04-17T00:00:00Z
review text: The paper deals with finite basis problem for classes of partition semigroups considered as involutary semigroups. A number of interesting results are obtained. The technique relies on a subtle analysis of the structure of the semigroups under consideration as well as on the results of a previous paper by the same authors [J. Eur. Math. Soc. (JEMS) 14, No. 3, 937-969 (2012; Zbl 1261.20068)]. It is in particular proved that the following involutive semigroups are not finitely based: the full partition semigroup \(\mathfrak C_n\) for \(n\geq 2\), the Brauer semigroup \(\mathfrak B_n\) for \(n\geq 4\), the partial Brauer semigroup \(P\mathfrak B_n\) for \(n\geq 3\), the annular semigroup \(\mathfrak U_n\) for \(n\geq 4\), \(n\) even or a prime power. It is also proved that, with respect to the `skew' involution, for each \(n\geq 4\) the semigroups \(\mathfrak B_n\), \(\mathfrak U_n\) and also the Jones semigroup \(\mathfrak J_n\) are inherently nonfinitely based. In addition, it is shown that similar techniques apply to the finite basis problem for existence varieties of locally inverse semigroups.
reviewed by: Ganna Kudryavtseva
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 6155229
zbMATH Keywords: nonfinitely based varieties
zbMATH Keywords: involutory semigroups
zbMATH Keywords: partition semigroups
zbMATH Keywords: existence varieties
zbMATH Keywords: finite basis problem
zbMATH Keywords: varieties of semigroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.06.021
OpenAlex ID: W2007614225
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DOI: 10.1016/J.JALGEBRA.2012.06.021
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description: scientific article; zbMATH DE number 6155229