Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subs...

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Main Authors:	Kritsada Sangkhanan, Jintana Sanwong
Format:	Journal
Published:	2020
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079147994&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68451
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Institution:	Chiang Mai University

id	th-cmuir.6653943832-68451
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spelling	th-cmuir.6653943832-684512020-04-02T15:27:37Z Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence Kritsada Sangkhanan Jintana Sanwong Mathematics © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subsemigroup TE(X, Y) of T(X, Y) by TE(X,Y)={α∈T(X,Y):∀(x,y)∈E,(xα,yα)∈E}.Then TE(X, Y) is the semigroup of all continuous self-maps of the topological space X for which all E-classes form a basis carrying X into a subspace Y. In this paper, we give a necessary and sufficient condition for TE(X, Y) to be regular and characterize Green’s relations on TE(X, Y). Our work extends previous results found in the literature. 2020-04-02T15:27:37Z 2020-04-02T15:27:37Z 2020-04-01 Journal 14322137 00371912 2-s2.0-85079147994 10.1007/s00233-020-10089-3 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079147994&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68451
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Kritsada Sangkhanan Jintana Sanwong Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
description	© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subsemigroup TE(X, Y) of T(X, Y) by TE(X,Y)={α∈T(X,Y):∀(x,y)∈E,(xα,yα)∈E}.Then TE(X, Y) is the semigroup of all continuous self-maps of the topological space X for which all E-classes form a basis carrying X into a subspace Y. In this paper, we give a necessary and sufficient condition for TE(X, Y) to be regular and characterize Green’s relations on TE(X, Y). Our work extends previous results found in the literature.
format	Journal
author	Kritsada Sangkhanan Jintana Sanwong
author_facet	Kritsada Sangkhanan Jintana Sanwong
author_sort	Kritsada Sangkhanan
title	Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
title_short	Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
title_full	Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
title_fullStr	Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
title_full_unstemmed	Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
title_sort	regularity and green’s relations on semigroups of transformations with restricted range that preserve an equivalence
publishDate	2020
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079147994&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68451
_version_	1681426822392184832

Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence

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