On (finite) distributive lattices with antitone involutions.
type: Item
instance of: scholarly article
title: On (finite) distributive lattices with antitone involutions.
zbMATH Open document ID: 1330.06004
author: Michal Botur
author: Jan Kühr
published in: Soft Computing
publication date: 2015-12-02T00:00:00Z
review text: Basic algebras are equivalent to bounded lattices with sectional antitone involutions. If this lattice is distributive, the assigned basic algebra is called distributive. It is proved that for every finite distributive basic algebra its underlying lattice is a direct product of chains. Every so-called weakly monotone basic algebra is distributive. Moreover, every finite weakly monotone basic algebra is an MV-algebra. Sharp elements in weakly monotone basic algebras are studied. For every weakly monotone basic algebra \(A\), the set \(S(A)\) of its sharp elements is a subalgbera of \(A\) which is in fact a Boolean algebra. Direct decompositions of weakly monotone basic algebras are characterized.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 6515462
zbMATH Keywords: distributive lattices with involution
zbMATH Keywords: De Morgan algebras
zbMATH Keywords: basic algebras
zbMATH Keywords: MV-algebras
zbMATH Keywords: sharp elements
zbMATH Keywords: weakly monotone basic algebras
zbMATH Keywords: distributive basic algebras
reviewed by: Ivan Chajda
MaRDI profile type: Publication
full work available at URL: s00500-013-1205-5
OpenAlex ID: W2097678272
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DOI: 10.1007/S00500-013-1205-5
description: scientific article; zbMATH DE number 6515462