Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets

© Tübitak. Let Y be a fixed subset of a nonempty set X and let Fix(X, Y ) be the set of all self maps on X which fix all elements in Y . Then under the composition of maps, Fix(X, Y ) is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of Fix (X, Y )...

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Main Authors:	Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Format:	Journal
Published:	2018
Subjects:	Agricultural and Biological Sciences
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85010496928&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47015
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-470152018-04-25T07:30:29Z Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets Yanisa Chaiya Preeyanuch Honyam Jintana Sanwong Agricultural and Biological Sciences © Tübitak. Let Y be a fixed subset of a nonempty set X and let Fix(X, Y ) be the set of all self maps on X which fix all elements in Y . Then under the composition of maps, Fix(X, Y ) is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of Fix (X, Y ) and these maximal subsemigroups coincide with the maximal regular subsemigroups when X \ Y is a finite set with \|X \ Y \| ≥ 2. We also give necessary and sufficient conditions for Fix(X, Y ) to be factorizable, unit-regular, and directly finite. 2018-04-25T07:09:20Z 2018-04-25T07:09:20Z 2017-01-01 Journal 13036149 13000098 2-s2.0-85010496928 10.3906/mat-1507-7 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85010496928&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47015
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Agricultural and Biological Sciences
spellingShingle	Agricultural and Biological Sciences Yanisa Chaiya Preeyanuch Honyam Jintana Sanwong Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
description	© Tübitak. Let Y be a fixed subset of a nonempty set X and let Fix(X, Y ) be the set of all self maps on X which fix all elements in Y . Then under the composition of maps, Fix(X, Y ) is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of Fix (X, Y ) and these maximal subsemigroups coincide with the maximal regular subsemigroups when X \ Y is a finite set with \|X \ Y \| ≥ 2. We also give necessary and sufficient conditions for Fix(X, Y ) to be factorizable, unit-regular, and directly finite.
format	Journal
author	Yanisa Chaiya Preeyanuch Honyam Jintana Sanwong
author_facet	Yanisa Chaiya Preeyanuch Honyam Jintana Sanwong
author_sort	Yanisa Chaiya
title	Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
title_short	Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
title_full	Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
title_fullStr	Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
title_full_unstemmed	Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
title_sort	maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85010496928&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47015
_version_	1681422982120996864

Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets

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