Vernitski, Alexei (2008) Ordered and J-trivial semigroups as divisors of semigroups of languages. International Journal of Algebra and Computation, 18 (07). pp. 1223-1229. DOI https://doi.org/10.1142/s021819670800486x
Vernitski, Alexei (2008) Ordered and J-trivial semigroups as divisors of semigroups of languages. International Journal of Algebra and Computation, 18 (07). pp. 1223-1229. DOI https://doi.org/10.1142/s021819670800486x
Vernitski, Alexei (2008) Ordered and J-trivial semigroups as divisors of semigroups of languages. International Journal of Algebra and Computation, 18 (07). pp. 1223-1229. DOI https://doi.org/10.1142/s021819670800486x
Abstract
A semigroup of languages is a set of languages considered with (and closed under) the operation of catenation. In other words, semigroups of languages are subsemigroups of power-semigroups of free semigroups. We prove that a (finite) semigroup is positively ordered if and only if it is a homomorphic image, under an order-preserving homomorphism, of a (finite) semigroup of languages. Hence it follows that a finite semigroup is J -trivial if and only if it is a homomorphic image of a finite semigroup of languages.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Product of languages; catenation of languages; semigroup of languages; monoid of languages; J -trivial semigroup; J -trivial monoid; positively ordered semigroup; ordered monoid |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 04 Jan 2012 11:06 |
| Last Modified: | 30 Oct 2024 20:07 |
| URI: | http://repository.essex.ac.uk/id/eprint/1803 |