On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
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| Creator |
Catarino, P.
Higgins, P.M. Levi, I. |
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| Description |
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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| Date |
2019-06-15T11:42:40Z
2019-06-15T11:42:40Z 2015 |
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| Type |
Article
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| Identifier |
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.
1726-3255 2010 MSC:20M20, 05C25. http://dspace.nbuv.gov.ua/handle/123456789/154250 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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