On Semigroups of Orientation-preserving Transformations with Restricted Range
© 2016, Taylor & Francis Group, LLC. Let X n be a chain with n elements (n ∈ ℕ), and let & #x1D4AA; & #x1D4AB; n be the monoid of all orientation-preserving transformations of X n . In this article, for any nonempty subset Y of X n , we consider the subsemigroup &...
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th-cmuir.6653943832-426242017-09-28T04:28:06Z On Semigroups of Orientation-preserving Transformations with Restricted Range Fernandes V. Honyam P. Quinteiro T. Singha B. © 2016, Taylor & Francis Group, LLC. Let X n be a chain with n elements (n ∈ ℕ), and let & #x1D4AA; & #x1D4AB; n be the monoid of all orientation-preserving transformations of X n . In this article, for any nonempty subset Y of X n , we consider the subsemigroup & #x1D4AA; & #x1D4AB; n (Y) of & #x1D4AA; & #x1D4AB; n of all transformations with range contained in Y: We describe the largest regular subsemigroup of & #x1D4AA; & #x1D4AB; n (Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type & #x1D4AA; & #x1D4AB; n (Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid & #x1D4AA;ℛ n of all either orientation-preserving or orientation-reversing transformations of X n . 2017-09-28T04:28:05Z 2017-09-28T04:28:05Z 2016-01-01 Journal 00927872 2-s2.0-84944790117 10.1080/00927872.2014.975345 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84944790117&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/42624 |
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© 2016, Taylor & Francis Group, LLC. Let X n be a chain with n elements (n ∈ ℕ), and let & #x1D4AA; & #x1D4AB; n be the monoid of all orientation-preserving transformations of X n . In this article, for any nonempty subset Y of X n , we consider the subsemigroup & #x1D4AA; & #x1D4AB; n (Y) of & #x1D4AA; & #x1D4AB; n of all transformations with range contained in Y: We describe the largest regular subsemigroup of & #x1D4AA; & #x1D4AB; n (Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type & #x1D4AA; & #x1D4AB; n (Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid & #x1D4AA;ℛ n of all either orientation-preserving or orientation-reversing transformations of X n . |
| format |
Journal |
| author |
Fernandes V. Honyam P. Quinteiro T. Singha B. |
| spellingShingle |
Fernandes V. Honyam P. Quinteiro T. Singha B. On Semigroups of Orientation-preserving Transformations with Restricted Range |
| author_facet |
Fernandes V. Honyam P. Quinteiro T. Singha B. |
| author_sort |
Fernandes V. |
| title |
On Semigroups of Orientation-preserving Transformations with Restricted Range |
| title_short |
On Semigroups of Orientation-preserving Transformations with Restricted Range |
| title_full |
On Semigroups of Orientation-preserving Transformations with Restricted Range |
| title_fullStr |
On Semigroups of Orientation-preserving Transformations with Restricted Range |
| title_full_unstemmed |
On Semigroups of Orientation-preserving Transformations with Restricted Range |
| title_sort |
on semigroups of orientation-preserving transformations with restricted range |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84944790117&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/42624 |
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