\(F\)-regular semigroups.
type: Item
instance of: scholarly article
title: \(F\)-regular semigroups.
zbMATH Open document ID: 1060.20051
author: P. Marques-Smith
author: Emilia Giraldes
author: H. Mitsch
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: A regular semigroup \(S\) is called \(F\)-regular if there exists a group congruence \(\rho\) on \(S\) such that every \(\rho\)-class contains a greatest element with respect to the natural partial order on \(S\). Continuing many investigations of \(F\)-regular semigroups, the authors characterize them and give a new representation of such semigroups by means of so called Szendrei triples. In particular, \(F\)-inverse semigroups (introduced by V. V. Wagner) are characterized.
reviewed by: Grigori I. Zhitomirski
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 2105358
zbMATH Keywords: regular semigroups
zbMATH Keywords: \(F\)-semigroups
zbMATH Keywords: inverse semigroups
zbMATH Keywords: group congruences
zbMATH Keywords: semidirect products
zbMATH Keywords: strictly combinatorial semigroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.050
OpenAlex ID: W2076366839
cites work: Perfect Dubreil-Jacotin semigroups
cites work: Perfect elements in Dubreil-Jacotin regular semigroups
cites work: Unit orthodox semigroups
cites work: Principally ordered regular semigroups
cites work: F-regular and F-orthodox semigroups
cites work: Q4839155
cites work: \(F\)-abundant semigroups
cites work: Almost factorisable inverse semigroups
cites work: Groups, Semilattices and Inverse Semigroups. II
cites work: E-unitary inverse semigroups over semilattices
cites work: F-Inverse Semigroups
cites work: A Natural Partial Order for Semigroups
cites work: Q3337662
cites work: The natural partial order on a regular semigroup
cites work: Q3767514
DOI: 10.1016/J.JALGEBRA.2003.09.050
Recommended article: Q3607828
Recommended article: Regular F-Abundant Semigroups
Recommended article: A representation for \(F\)-regular semigroups.
Recommended article: \(\mathcal P\)-regular semigroups.
Recommended article: Q3369852
Recommended article: Finitely Generated Commutative Regular Semigroups
Recommended article: Q3009721
Recommended article: Q3426079
Recommended article: Regular semigroups with a regular *-transversal.
Recommended article: Q3641469
description: scientific article; zbMATH DE number 2105358