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.6653943832-71202014-08-30T03:51:36Z Regularity in semigroups of transformations with invariant sets Choomanee W. Honyam P. Sanwong J. 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. 2014-08-30T03:51:36Z 2014-08-30T03:51:36Z 2013 Article 13118080 10.12732/ijpam.v87i1.9 http://www.scopus.com/inward/record.url?eid=2-s2.0-84882965960&partnerID=40&md5=848afa282e9cf076778df1e23d02556f http://cmuir.cmu.ac.th/handle/6653943832/7120 English |
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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 |
Article |
| author |
Choomanee W. Honyam P. Sanwong J. |
| spellingShingle |
Choomanee W. Honyam P. Sanwong J. Regularity in semigroups of transformations with invariant sets |
| author_facet |
Choomanee W. Honyam P. Sanwong J. |
| author_sort |
Choomanee W. |
| 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 |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-84882965960&partnerID=40&md5=848afa282e9cf076778df1e23d02556f http://cmuir.cmu.ac.th/handle/6653943832/7120 |
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1681420741273190400 |