Research Repository

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). pp. 4319-4335. ISSN 0092-7872

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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
Uncontrolled Keywords: Filter; Ideal; Lattice; Quasiorder; Semigroup
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Jan 2012 11:29
Last Modified: 15 Jan 2022 00:36

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