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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-57949087617&partnerID=40&md5=1b48759ab6ee6c2e1f8a2246e47ea842 http://cmuir.cmu.ac.th/handle/6653943832/5334 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | 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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