Semigroups of transformations with invariant set
Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a xed nonempty subset Y of X, let S(X, Y) = {α ε T(X): Y α ⊆ Y} Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) i...
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th-cmuir.6653943832-430822017-09-28T06:47:31Z Semigroups of transformations with invariant set Honyam P. Sanwong J. Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a xed nonempty subset Y of X, let S(X, Y) = {α ε T(X): Y α ⊆ Y} Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S(A 1 ;A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals. © 2011 The Korean Mathematical Society. 2017-09-28T06:47:31Z 2017-09-28T06:47:31Z 2011-03-18 Journal 03049914 2-s2.0-79952597964 10.4134/JKMS.2011.48.2.289 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79952597964&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43082 |
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Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a xed nonempty subset Y of X, let S(X, Y) = {α ε T(X): Y α ⊆ Y} Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S(A 1 ;A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals. © 2011 The Korean Mathematical Society. |
| format |
Journal |
| author |
Honyam P. Sanwong J. |
| spellingShingle |
Honyam P. Sanwong J. Semigroups of transformations with invariant set |
| author_facet |
Honyam P. Sanwong J. |
| author_sort |
Honyam P. |
| title |
Semigroups of transformations with invariant set |
| title_short |
Semigroups of transformations with invariant set |
| title_full |
Semigroups of transformations with invariant set |
| title_fullStr |
Semigroups of transformations with invariant set |
| title_full_unstemmed |
Semigroups of transformations with invariant set |
| title_sort |
semigroups of transformations with invariant set |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79952597964&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43082 |
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1681422311306035200 |