Words on free bands with inverse transversals.
type: Item
instance of: scholarly article
title: Words on free bands with inverse transversals.
zbMATH Open document ID: 1341.20061
author: Xilin Tang
author: Ze Gu
published in: Semigroup Forum
publication date: 2015-12-09T00:00:00Z
review text: An inverse transversal \(T\) of a regular semigroup \(S\) is an inverse subsemigroup with the property that each element \(a\) of \(S\) has a unique inverse \(a^0\) belonging to \(T\). The unary operation so defined turns \(S\) into a regular unary semigroup. The first author [Commun. Algebra 36, No. 7, 2487-2502 (2008; Zbl 1157.20036)] found a set of identities that define the regular semigroups with inverse transversal within the variety of all regular unary semigroups. Their algebraic study had originated with \textit{T. S. Blyth} and \textit{R. McFadden} [Proc. R. Soc. Edinb., Sect. A, Math. 92, 253-270 (1982; Zbl 0507.20026)]. The purpose of this paper is to solve the word problem for the free objects in the subvariety consisting of the bands with inverse (that is, semilattice) transversal. While the solution might have been achieved more simply by adapting the standard methods for the free band itself, they are sufficiently practical to enable calculation of the cardinalities of the \(\mathcal D\)-classes, for instance. Integral to their solution is the solution to the word problem in the subvariety of right regular bands with semilattice transversal.
reviewed by: Peter R. Jones
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 6518141
zbMATH Keywords: varieties of regular semigroups
zbMATH Keywords: regular unary semigroups
zbMATH Keywords: word problem
zbMATH Keywords: inverse transversals
zbMATH Keywords: semilattice transversals
zbMATH Keywords: free bands
zbMATH Keywords: free IST-bands
zbMATH Keywords: IST-varieties
MaRDI profile type: Publication
full work available at URL: s00233-014-9645-5
OpenAlex ID: W2012969630
cites work: Regular semigroups with a multiplicative inverse transversal
cites work: A CLASSIFICATION OF INVERSE TRANSVERSALS
cites work: The lattice of equational classes of idempotent semigroups
cites work: Identities for existence varieties of regular semigroups
cites work: A new approach in the theory of orthodox semigroups
cites work: Regular semigroups with inverse transversals
cites work: Identities for a Class of Regular Unary Semigroups
cites work: Free orthodox semigroups and free bands with inverse transversals.
cites work: Congruences on regular semigroups with inverse transversals*
DOI: 10.1007/S00233-014-9645-5
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description: scientific article; zbMATH DE number 6518141