Regularity in semigroups of transformations with invariant sets
Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intr...
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th-cmuir.6653943832-476942018-04-25T08:42:56Z Regularity in semigroups of transformations with invariant sets Wanida Choomanee Preeyanuch Honyam Jintana Sanwong Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements. Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set. © 2013 Academic Publications, Ltd. 2018-04-25T08:42:56Z 2018-04-25T08:42:56Z 2013-08-30 Journal 13143395 13118080 2-s2.0-84882965960 10.12732/ijpam.v87i1.9 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47694 |
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Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements. Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set. © 2013 Academic Publications, Ltd. |
| format |
Journal |
| author |
Wanida Choomanee Preeyanuch Honyam Jintana Sanwong |
| spellingShingle |
Wanida Choomanee Preeyanuch Honyam Jintana Sanwong Regularity in semigroups of transformations with invariant sets |
| author_facet |
Wanida Choomanee Preeyanuch Honyam Jintana Sanwong |
| author_sort |
Wanida Choomanee |
| title |
Regularity in semigroups of transformations with invariant sets |
| title_short |
Regularity in semigroups of transformations with invariant sets |
| title_full |
Regularity in semigroups of transformations with invariant sets |
| title_fullStr |
Regularity in semigroups of transformations with invariant sets |
| title_full_unstemmed |
Regularity in semigroups of transformations with invariant sets |
| title_sort |
regularity in semigroups of transformations with invariant sets |
| publishDate |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47694 |
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1681423109605818368 |