Catarino, P and Higgins, PM and Levi, I (2015) 'On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations.' Algebra and Discrete Mathematics, 19 (2). 162 - 171. ISSN 1726-3255
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Abstract
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.
| Item Type: | Article |
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| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Health > Mathematical Sciences, Department of |
| Depositing User: | Jim Jamieson |
| Date Deposited: | 05 Mar 2015 14:50 |
| Last Modified: | 08 Aug 2019 12:15 |
| URI: | http://repository.essex.ac.uk/id/eprint/13220 |
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