\(\mathsf E\)-local pseudovarieties.
type: Item
instance of: scholarly article
title: \(\mathsf E\)-local pseudovarieties.
zbMATH Open document ID: 1279.20071
author: Ana Moura
published in: Semigroup Forum
publication date: 2012-11-08T00:00:00Z
review text: The author says that a pseudovariety \(\mathbf V\) of finite semigroups is \(\mathsf E\)-local if, for every finite semigroup \(S\), the subsemigroup generated by all idempotents of \(S\) lies in \(\mathbf V\) whenever, for each regular \(\mathcal D\)-class \(D\) of \(S\), the subsemigroup generated by all idempotents of \(D\) lies in \(\mathbf V\). She exhibits several examples of \(\mathsf E\)-local pseudovarieties; in particular, she observes that for every pseudovariety \(\mathbf H\) of finite groups, the class of all finite semigroups whose subgroups lie in \(\mathbf H\) forms an \(\mathsf E\)-local pseudovariety. Further, the author characterizes \(\mathsf E\)-local pseudovarieties that consist of finite semigroups in whose idempotent-generated subsemigroups each regular \(\mathcal D\)-class forms a subsemigroup. She also provides several sufficient conditions for a pseudoidentity to define an \(\mathsf E\)-local pseudovariety.
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 6103697
zbMATH Keywords: finite semigroups
zbMATH Keywords: idempotent-generated semigroups
zbMATH Keywords: regular \(\mathcal D\)-classes
zbMATH Keywords: operators
zbMATH Keywords: E-local pseudovarieties
zbMATH Keywords: pseudoidentities
MaRDI profile type: Publication
full work available at URL: s00233-012-9413-3
OpenAlex ID: W2066596605
cites work: Q4848740
cites work: Idempotent-generated semigroups and pseudovarieties
cites work: PROFINITE IDENTITIES FOR FINITE SEMIGROUPS WHOSE SUBGROUPS BELONG TO A GIVEN PSEUDOVARIETY
cites work: On inverses of products of idempotents in regular semigroups
cites work: On finite 0-simple semigroups and graph theory
cites work: The Birkhoff theorem for finite algebras
cites work: Q5302760
DOI: 10.1007/S00233-012-9413-3
description: scientific article; zbMATH DE number 6103697