Regularity and green's relations on a semigroup of transformations with restricted range
Let T(X) be the full transformation semigroup on the set X and let T (X), Y) = {α ∈ T (X) : X α ⊆ Y}. Then T(X, Y) is a sub-semigroup of T(X) determined by a nonempty subset Y of X. In this paper, we give a necessary and sufficient condition for T(X, Y) to be regular. In the case that T(X, Y) is not...
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th-cmuir.6653943832-605482018-09-10T03:44:53Z Regularity and green's relations on a semigroup of transformations with restricted range Jintana Sanwong Worachead Sommanee Mathematics Let T(X) be the full transformation semigroup on the set X and let T (X), Y) = {α ∈ T (X) : X α ⊆ Y}. Then T(X, Y) is a sub-semigroup of T(X) determined by a nonempty subset Y of X. In this paper, we give a necessary and sufficient condition for T(X, Y) to be regular. In the case that T(X, Y) is not regular, the largest regular sub-semigroup is obtained and this sub-semigroupis shown to determine the Green's relations on T(X, Y). Also, a class of maximal inverse sub-semigroups of T(X, Y) is obtained. Copyright © 2008 J. Sanwong and W. Sommanee. 2018-09-10T03:44:53Z 2018-09-10T03:44:53Z 2008-12-30 Journal 16870425 01611712 2-s2.0-57949087617 10.1155/2008/794013 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=57949087617&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60548 |
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Mathematics |
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Mathematics Jintana Sanwong Worachead Sommanee Regularity and green's relations on a semigroup of transformations with restricted range |
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Let T(X) be the full transformation semigroup on the set X and let T (X), Y) = {α ∈ T (X) : X α ⊆ Y}. Then T(X, Y) is a sub-semigroup of T(X) determined by a nonempty subset Y of X. In this paper, we give a necessary and sufficient condition for T(X, Y) to be regular. In the case that T(X, Y) is not regular, the largest regular sub-semigroup is obtained and this sub-semigroupis shown to determine the Green's relations on T(X, Y). Also, a class of maximal inverse sub-semigroups of T(X, Y) is obtained. Copyright © 2008 J. Sanwong and W. Sommanee. |
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Journal |
| author |
Jintana Sanwong Worachead Sommanee |
| author_facet |
Jintana Sanwong Worachead Sommanee |
| author_sort |
Jintana Sanwong |
| title |
Regularity and green's relations on a semigroup of transformations with restricted range |
| title_short |
Regularity and green's relations on a semigroup of transformations with restricted range |
| title_full |
Regularity and green's relations on a semigroup of transformations with restricted range |
| title_fullStr |
Regularity and green's relations on a semigroup of transformations with restricted range |
| title_full_unstemmed |
Regularity and green's relations on a semigroup of transformations with restricted range |
| title_sort |
regularity and green's relations on a semigroup of transformations with restricted range |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=57949087617&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60548 |
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