Congruence relations on De Morgan algebras
type: Item
instance of: scholarly article
title: Congruence relations on De Morgan algebras
zbMATH Open document ID: 0674.06011
DOI: 10.1007/BF01243876
author: S. H. Smith
published in: Algebra Universalis
publication date: 1989-01-01T00:00:00Z
review text: A de Morgan algebra is an algebra (L;\(\vee,\wedge,\sim,0,1)\) of type (2,2,1,0,0) such that (L;\(\vee,\wedge,0,1)\) is a distributive (0,1)- lattice, \(\sim\) is a dual (0,1)-lattice endomorphism (so that \(\sim (a\vee b)=\sim a\wedge \sim b\), \(\sim (a\wedge b)=\sim a\vee \sim b\), \(\sim 0=1\), and \(\sim 1=0)\), and \(\sim \sim a=a)\). In the present paper various classes of de Morgan algebras are investigated whose congruence relations satisfy special conditions together with their interrelationship. In particular, the classes of congruence permutable, congruence regular, and congruence uniform de Morgan algebras are studied.
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 4103146
zbMATH Keywords: Priestley duality
zbMATH Keywords: De Morgan algebra
zbMATH Keywords: congruence relations
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01243876
OpenAlex ID: W2006995727
description: scientific article; zbMATH DE number 4103146