Green's relations and regularity for semigroups of transformations that preserve double direction equivalence.
type: Item
instance of: scholarly article
title: Green's relations and regularity for semigroups of transformations that preserve double direction equivalence.
zbMATH Open document ID: 1198.20053
author: Lunzhi Deng
author: Jiwen Zeng
author: Bo Xu
published in: Semigroup Forum
publication date: 2010-07-06T00:00:00Z
review text: For a set \(X\) and an equivalence relation \(E\) on \(X\) the authors study the subsemigroup \(T_E(X)\) of all full transformations \(f\) on \(X\) satisfying the condition that for any two elements \(x,y\in X\) we have \((x,y)\in E\) if and only if \((f(x),f(y))\in E\). The authors describe Green's relations for \(T_E(X)\) in combinatorial terms and discuss regularity of elements in \(T_E(X)\). In particular, it is shown that \(T_E(X)\) is regular if and only if \(|X/E|\) is finite.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 5730952
zbMATH Keywords: Green relations
zbMATH Keywords: regular semigroups
zbMATH Keywords: regular elements
zbMATH Keywords: semigroups of transformations
MaRDI profile type: Publication
full work available at URL: s00233-009-9204-7
OpenAlex ID: W4255685265
cites work: Q4003180
cites work: Q4126563
cites work: Green's Relations for Regular Elements of Semigroups of Endomorphisms
cites work: REGULARITY AND GREEN'S RELATIONS FOR SEMIGROUPS OF TRANSFORMATIONS THAT PRESERVE AN EQUIVALENCE
cites work: On the rank of the semigroup \(T_E(X)\)
DOI: 10.1007/S00233-009-9204-7
description: scientific article; zbMATH DE number 5730952