Juhasz, Z and Vernitski, Alexei (2011) Filters in (Quasiordered) Semigroups and Lattices of Filters. Communications in Algebra, 39 (11). pp. 4319-4335. DOI https://doi.org/10.1080/00927872.2010.523444
Juhasz, Z and Vernitski, Alexei (2011) Filters in (Quasiordered) Semigroups and Lattices of Filters. Communications in Algebra, 39 (11). pp. 4319-4335. DOI https://doi.org/10.1080/00927872.2010.523444
Juhasz, Z and Vernitski, Alexei (2011) Filters in (Quasiordered) Semigroups and Lattices of Filters. Communications in Algebra, 39 (11). pp. 4319-4335. DOI https://doi.org/10.1080/00927872.2010.523444
Abstract
A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean).
Item Type: | Article |
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Uncontrolled Keywords: | Filter; Ideal; Lattice; Quasiorder; Semigroup |
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 11:29 |
Last Modified: | 30 Oct 2024 20:10 |
URI: | http://repository.essex.ac.uk/id/eprint/1807 |