Operators on the lattice of pseudovarieties of finite semigroups
type: Item
instance of: scholarly article
title: Operators on the lattice of pseudovarieties of finite semigroups
zbMATH Open document ID: 0913.20038
DOI: 10.1007/PL00005974
author: Shuhua Zhang
author: Norman R. Reilly
published in: Semigroup Forum
publication date: 1999-03-23T00:00:00Z
review text: On the lattice \(\mathbf{L(F)}\) of all pseudovarieties of finite semigroups the Mal'cev type operator \({\mathbf U}\mapsto{\mathbf U}M^+=L{\mathbf G}\circ{\mathbf U}\) (\(L{\mathbf G}\) denoting the pseudovariety of all local groups) and operators \(T_l^+\), \(T_r^+\), \(T^+\), \(K^+\), \(K_l^+\), \(K_r^+\), \(K_\iota^+\) are studied (each of which is defined in the above way, \(L{\mathbf G}\) being replaced with a certain sub-pseudovariety). Each of these operators comes from a radical congruence system on \(\mathbf F\). Various aspects of these operators are investigated. For example, pseudoidentity bases of \({\mathbf U}M^+\), \({\mathbf U}T_l^+\), etc., are presented in terms of pseudoidentity bases of \({\mathbf U}\). Moreover, each of these operators is shown to commute with the local operator \(L\) and the core operator \(C\).
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 1209921
zbMATH Keywords: lattices of pseudovarieties
zbMATH Keywords: Mal'cev products
zbMATH Keywords: radical congruence systems
zbMATH Keywords: pseudovarieties of finite semigroups
zbMATH Keywords: pseudoidentity bases
reviewed by: K. Auinger
MaRDI profile type: Publication
full work available at URL: pl00005974
OpenAlex ID: W1973658951
description: scientific article; zbMATH DE number 1209921