On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transform...
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| Datum: | 2015 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2015
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154250 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations / P. Catarino, P.M. Higgins, I. Levi// Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 162-171. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3. |
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