Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section
© 2019 by the Mathematical Association of Thailand. All rights reserved. Let X be an arbitrary nonempty set and T(X) the full transformation semigroup on X. For an equivalence relation E on X and a cross-section R of the partition X=E induced by E, let TE(X, R) = {α ∈ T(X): Rα = R and ∀x, y ∈, (x, y...
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th-cmuir.6653943832-679072020-04-02T15:10:41Z Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section Nares Sawatraksa Chaiwat Namnak Kritsada Sangkhanan Mathematics © 2019 by the Mathematical Association of Thailand. All rights reserved. Let X be an arbitrary nonempty set and T(X) the full transformation semigroup on X. For an equivalence relation E on X and a cross-section R of the partition X=E induced by E, let TE(X, R) = {α ∈ T(X): Rα = R and ∀x, y ∈, (x, y) ∈ E ⇒ (xα, yα) ∈ E}. Then the set Reg(TE(X, R)) of all regular elements of TE(X, R) is a regular sub- semigroup of T(X). In this paper, we describe Green’s relations for elements of the semigroup Reg(TE(X, R)). Also, we discuss the natural partial order on this semigroup and characterize when two elements in Reg(TE(X, R)) are related under this order. 2020-04-02T15:10:41Z 2020-04-02T15:10:41Z 2019-08-01 Journal 16860209 2-s2.0-85073390312 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073390312&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67907 |
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Mathematics Nares Sawatraksa Chaiwat Namnak Kritsada Sangkhanan Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
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© 2019 by the Mathematical Association of Thailand. All rights reserved. Let X be an arbitrary nonempty set and T(X) the full transformation semigroup on X. For an equivalence relation E on X and a cross-section R of the partition X=E induced by E, let TE(X, R) = {α ∈ T(X): Rα = R and ∀x, y ∈, (x, y) ∈ E ⇒ (xα, yα) ∈ E}. Then the set Reg(TE(X, R)) of all regular elements of TE(X, R) is a regular sub- semigroup of T(X). In this paper, we describe Green’s relations for elements of the semigroup Reg(TE(X, R)). Also, we discuss the natural partial order on this semigroup and characterize when two elements in Reg(TE(X, R)) are related under this order. |
| format |
Journal |
| author |
Nares Sawatraksa Chaiwat Namnak Kritsada Sangkhanan |
| author_facet |
Nares Sawatraksa Chaiwat Namnak Kritsada Sangkhanan |
| author_sort |
Nares Sawatraksa |
| title |
Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| title_short |
Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| title_full |
Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| title_fullStr |
Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| title_full_unstemmed |
Green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| title_sort |
green’s relations and natural partial order on the regular subsemigroup of transformations preserving an equivalence relation and fixed a cross-section |
| publishDate |
2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073390312&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67907 |
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1681426721956429824 |