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Filters in (Quasiordered) Semigroups and Lattices of Filters

Juhasz, Z and Vernitski, A (2011) 'Filters in (Quasiordered) Semigroups and Lattices of Filters.' Communications in Algebra, 39 (11). 4319 - 4335. ISSN 0092-7872

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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). © 2011 Copyright Taylor and Francis Group, LLC.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 11:29
Last Modified: 30 Jan 2019 16:17
URI: http://repository.essex.ac.uk/id/eprint/1807

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