The join of the pseudovarieties of \(\mathcal R\)-trivial and \(\mathcal L\)-trivial monoids
type: Item
instance of: scholarly article
title: The join of the pseudovarieties of \(\mathcal R\)-trivial and \(\mathcal L\)-trivial monoids
zbMATH Open document ID: 0687.20054
DOI: 10.1016/0022-4049(89)90125-4
author: Jorge Almeida
author: Assis Azevedo
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The pseudovariety described in the title was previously studied by \textit{R. König} [Rairo, Inf. Théor. 19, 233-260 (1985; Zbl 0571.20066)]. The authors answer the remaining formerly open questions about this pseudovariety. In particular, they characterize it using pseudoidentities, following the approach of \textit{J. Reiterman} [Algebra Univers. 14, 1-10 (1982; Zbl 0484.08007)]. Their first such description involves a single pseudoidentity in five variables. An alternative description is given involving a single pseudoidentity in three variables. This is shown to be minimal in the sense that no set of pseudoidentities on two variables can define the required pseudovariety.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 4125705
zbMATH Keywords: monoid
zbMATH Keywords: pseudovariety
zbMATH Keywords: pseudoidentities
reviewed by: Graham T. Clarke
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90125-4
OpenAlex ID: W1967493755
cites work: Some pseudovariety joins involving the pseudovariety of finite groups
cites work: Implicit operations on finite \({\mathcal J}\)-trivial semigroups and a conjecture of I. Simon
cites work: The algebra of implicit operations
cites work: On pseudovarieties, varieties of languages, filters of congruences, pseudoidentities and related topics
cites work: Q4296426
cites work: Q3807430
cites work: Q4132170
cites work: Q3688573
cites work: Q3776657
cites work: The Birkhoff theorem for finite algebras
cites work: On finite monoids having only trivial subgroups
cites work: Q4077455
description: scientific article; zbMATH DE number 4125705