Juhász, Zsófia and Vernitski, Alexei (2011) 'Using filters to describe congruences and band congruences of semigroups.' Semigroup Forum, 83 (2). pp. 320-334. ISSN 0037-1912

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Abstract

It is well known that the smallest semilattice congruence can be described via filters. We generalise this result to the smallest left (right) normal band congruences and also to arbitrary semilattice (left normal band, right normal band) congruences, describing them all via filters. To achieve this, we introduce filters relative to arbitrary quasiorders on a semigroup (traditional filters are filters relative to the smallest negative operation-compatible quasiorder). We study congruences which can be described via filters. We show that the lattice of semilattice (left normal band, right normal band) congruences is a homomorphic image of the lattice of negative (right negative, left negative) operation-compatible quasiorders. © 2011 Springer Science+Business Media, LLC.

Item Type:	Article
Uncontrolled Keywords:	Filter; Semilattice; Band; Congruence; Quasiorder; Preorder
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 11:32
Last Modified:	15 Jan 2022 00:36
URI:	http://repository.essex.ac.uk/id/eprint/1808

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