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On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Catarino, Paula Higgins, Peter M. Levi, Inessa |
| Copyright Year | 2015 |
| Abstract | It is well-known [16] that the semigroup \(\mathcal{T}_n\) of all total transformations of a given \(n\)-element set \(X_n\) 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 \(X_n\) is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of \(X_n\) 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 \(X_n\) are covered by their inverse subsemigroups precisely when \(n \leq 3\). |
| File Format | PDF HTM / HTML |
| Volume Number | 19 |
| Alternate Webpage(s) | http://adm.luguniv.edu.ua/downloads/issues/2015/N2/adm-n2(2015)-2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
