Semigroups of transformations with fixed sets
Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's r...
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th-cmuir.6653943832-71772014-08-30T03:51:40Z Semigroups of transformations with fixed sets Honyam P. Sanwong J. Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's relations and ideals of Fix(X, Y) and prove that Fix(X, Y) is never isomorphic to T (Z) for any set Z when ∅ ≠ Y ⊈ X. However, its rank is related to the rank of T (X\Y) and the cardinality of Y when X is a finite set. © 2013 Copyright NISC Pty Ltd. 2014-08-30T03:51:40Z 2014-08-30T03:51:40Z 2013 Article 16073606 10.2989/16073606.2013.779958 http://www.scopus.com/inward/record.url?eid=2-s2.0-84876029745&partnerID=40&md5=f203d57f7532c81c4612d23e2c1b05e4 http://cmuir.cmu.ac.th/handle/6653943832/7177 English |
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Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's relations and ideals of Fix(X, Y) and prove that Fix(X, Y) is never isomorphic to T (Z) for any set Z when ∅ ≠ Y ⊈ X. However, its rank is related to the rank of T (X\Y) and the cardinality of Y when X is a finite set. © 2013 Copyright NISC Pty Ltd. |
| format |
Article |
| author |
Honyam P. Sanwong J. |
| spellingShingle |
Honyam P. Sanwong J. Semigroups of transformations with fixed sets |
| author_facet |
Honyam P. Sanwong J. |
| author_sort |
Honyam P. |
| title |
Semigroups of transformations with fixed sets |
| title_short |
Semigroups of transformations with fixed sets |
| title_full |
Semigroups of transformations with fixed sets |
| title_fullStr |
Semigroups of transformations with fixed sets |
| title_full_unstemmed |
Semigroups of transformations with fixed sets |
| title_sort |
semigroups of transformations with fixed sets |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-84876029745&partnerID=40&md5=f203d57f7532c81c4612d23e2c1b05e4 http://cmuir.cmu.ac.th/handle/6653943832/7177 |
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1681420751769436160 |