The regular part of a semigroup of transformations with restricted range

Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that F(X, Y)={αT(X, Y): Xα⊆ Y=α}, is the largest regular subsemigroup of T(X,Y) and determines Green's relations on T...

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Main Author: Sanwong J.
Format: Article
Language:English
Published: 2014
Online Access:http://www.scopus.com/inward/record.url?eid=2-s2.0-80051547466&partnerID=40&md5=a46e20848ed71a6fac9ad2456950ca3f
http://cmuir.cmu.ac.th/handle/6653943832/6478
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Institution: Chiang Mai University
Language: English
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spelling th-cmuir.6653943832-64782014-08-30T03:24:16Z The regular part of a semigroup of transformations with restricted range Sanwong J. Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that F(X, Y)={αT(X, Y): Xα⊆ Y=α}, is the largest regular subsemigroup of T(X,Y) and determines Green's relations on T(X,Y). In this paper, we show that F(X,Y)≅T(Z) if and only if X=Y and {pipe}Y{pipe}={pipe}Z{pipe}; or {pipe}Y{pipe}=1={pipe}Z{pipe}, and prove that every regular semigroup S can be embedded in F(S1,S). Then we describe Green's relations and ideals of F(X,Y) and apply these results to get all of its maximal regular subsemigroups when Y is a nonempty finite subset of X. © 2011 Springer Science+Business Media, LLC. 2014-08-30T03:24:16Z 2014-08-30T03:24:16Z 2011 Article 371912 10.1007/s00233-011-9320-z http://www.scopus.com/inward/record.url?eid=2-s2.0-80051547466&partnerID=40&md5=a46e20848ed71a6fac9ad2456950ca3f http://cmuir.cmu.ac.th/handle/6653943832/6478 English
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
language English
description Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that F(X, Y)={αT(X, Y): Xα⊆ Y=α}, is the largest regular subsemigroup of T(X,Y) and determines Green's relations on T(X,Y). In this paper, we show that F(X,Y)≅T(Z) if and only if X=Y and {pipe}Y{pipe}={pipe}Z{pipe}; or {pipe}Y{pipe}=1={pipe}Z{pipe}, and prove that every regular semigroup S can be embedded in F(S1,S). Then we describe Green's relations and ideals of F(X,Y) and apply these results to get all of its maximal regular subsemigroups when Y is a nonempty finite subset of X. © 2011 Springer Science+Business Media, LLC.
format Article
author Sanwong J.
spellingShingle Sanwong J.
The regular part of a semigroup of transformations with restricted range
author_facet Sanwong J.
author_sort Sanwong J.
title The regular part of a semigroup of transformations with restricted range
title_short The regular part of a semigroup of transformations with restricted range
title_full The regular part of a semigroup of transformations with restricted range
title_fullStr The regular part of a semigroup of transformations with restricted range
title_full_unstemmed The regular part of a semigroup of transformations with restricted range
title_sort regular part of a semigroup of transformations with restricted range
publishDate 2014
url http://www.scopus.com/inward/record.url?eid=2-s2.0-80051547466&partnerID=40&md5=a46e20848ed71a6fac9ad2456950ca3f
http://cmuir.cmu.ac.th/handle/6653943832/6478
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