Regularity in semigroups of transformations with invariant sets

Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intr...

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Main Authors:	Wanida Choomanee, Preeyanuch Honyam, Jintana Sanwong
Format:	Journal
Published:	2018
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/52745
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-527452018-09-04T09:31:24Z Regularity in semigroups of transformations with invariant sets Wanida Choomanee Preeyanuch Honyam Jintana Sanwong Mathematics Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements. Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set. © 2013 Academic Publications, Ltd. 2018-09-04T09:31:24Z 2018-09-04T09:31:24Z 2013-08-30 Journal 13143395 13118080 2-s2.0-84882965960 10.12732/ijpam.v87i1.9 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/52745
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Wanida Choomanee Preeyanuch Honyam Jintana Sanwong Regularity in semigroups of transformations with invariant sets
description	Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements. Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set. © 2013 Academic Publications, Ltd.
format	Journal
author	Wanida Choomanee Preeyanuch Honyam Jintana Sanwong
author_facet	Wanida Choomanee Preeyanuch Honyam Jintana Sanwong
author_sort	Wanida Choomanee
title	Regularity in semigroups of transformations with invariant sets
title_short	Regularity in semigroups of transformations with invariant sets
title_full	Regularity in semigroups of transformations with invariant sets
title_fullStr	Regularity in semigroups of transformations with invariant sets
title_full_unstemmed	Regularity in semigroups of transformations with invariant sets
title_sort	regularity in semigroups of transformations with invariant sets
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/52745
_version_	1681424007221477376

Regularity in semigroups of transformations with invariant sets

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