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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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2017
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| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | © 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 . |
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