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: Jintana Sanwong
Format: Journal
Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/50119
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spelling th-cmuir.6653943832-501192018-09-04T04:24:36Z The regular part of a semigroup of transformations with restricted range Jintana Sanwong Mathematics 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. 2018-09-04T04:24:36Z 2018-09-04T04:24:36Z 2011-08-01 Journal 00371912 2-s2.0-80051547466 10.1007/s00233-011-9320-z https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=80051547466&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50119
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Jintana Sanwong
The regular part of a semigroup of transformations with restricted range
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 Journal
author Jintana Sanwong
author_facet Jintana Sanwong
author_sort Jintana Sanwong
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 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=80051547466&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/50119
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