The regular part of a semigroup of transformations with restricted range.
type: Item
instance of: scholarly article
title: The regular part of a semigroup of transformations with restricted range.
zbMATH Open document ID: 1243.20075
author: Jintana Sanwong
published in: Semigroup Forum
publication date: 2012-03-23T00:00:00Z
review text: Let \(X\) be a set and \(T(X)\) the semigroup of all transformations of \(X\). For \(Y\subset X\) let \(F(X,Y)\) be the subsemigroup consisting of all transformations \(f\) satisfying \(f(X)=f(Y)\subset Y\). In the paper under review the author describes Green's relations and ideals of \(F(X,Y)\). As a corollary, in the case of non-empty finite \(Y\) the author describes all maximal regular subsemigroups of \(F(X,Y)\). Furthermore, the authors determines all cases in which \(F(X,Y)\) is isomorphic to the full transformation semigroup on some set and shows that every regular semigroup \(S\) embeds into \(F(S^1,S)\).
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 6018058
zbMATH Keywords: transformation semigroups
zbMATH Keywords: Green relations
zbMATH Keywords: images
zbMATH Keywords: regular subsemigroups
MaRDI profile type: Publication
full work available at URL: s00233-011-9320-z
OpenAlex ID: W2037745397
cites work: Q3848243
cites work: Q5564342
cites work: Q4126563
cites work: Regularity and Green's relations on a semigroup of transformations with restricted range.
cites work: Maximal and minimal congruences on some semigroups.
cites work: Some results concerning a transformation semigroup
cites work: Maximal regular subsemigroups of certain semigroups of transformations
DOI: 10.1007/S00233-011-9320-Z
description: scientific article; zbMATH DE number 6018058