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: | , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| 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 |
| Summary: | © 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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