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.6653943832-480712018-04-25T08:47:23Z Semigroups of transformations with fixed sets Preeyanuch Honyam Jintana Sanwong 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. 2018-04-25T08:47:22Z 2018-04-25T08:47:22Z 2013-03-01 Journal 1727933X 16073606 2-s2.0-84876029745 10.2989/16073606.2013.779958 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84876029745&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/48071 |
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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 |
Journal |
| author |
Preeyanuch Honyam Jintana Sanwong |
| spellingShingle |
Preeyanuch Honyam Jintana Sanwong Semigroups of transformations with fixed sets |
| author_facet |
Preeyanuch Honyam Jintana Sanwong |
| author_sort |
Preeyanuch Honyam |
| 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 |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84876029745&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/48071 |
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