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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th-cmuir.6653943832-408652017-09-28T04:14:14Z Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets Chaiya Y. Honyam P. Sanwong J. © 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. 2017-09-28T04:14:14Z 2017-09-28T04:14:14Z 2017-01-01 Journal 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/6653943832/40865 |
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© 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. |
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Journal |
| author |
Chaiya Y. Honyam P. Sanwong J. |
| spellingShingle |
Chaiya Y. Honyam P. Sanwong J. Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets |
| author_facet |
Chaiya Y. Honyam P. Sanwong J. |
| author_sort |
Chaiya Y. |
| 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 |
2017 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85010496928&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40865 |
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