Weakly divisible MV-algebras and product
type: Item
instance of: scholarly article
title: Weakly divisible MV-algebras and product
zbMATH Open document ID: 0942.06003
author: Anatolij Dvurečenskij
author: Beloslav Riečan
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-10T00:00:00Z
review text: The authors prove that any weakly divisible \(\sigma\)-complete (and hence divisible) MV-algebra \(M\) is isomorphic, as an MV-algebra, with the set of all continuous fuzzy subsets defined on the set of maximal ideals of \(M\). They use this to define on \(M\) an associative, commutative product with \(1\) as the identity. As a result, any system of observables on \(M\) admits a unique joint observable with respect to this product.
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 1309055
zbMATH Keywords: weakly divisible MV-algebras
zbMATH Keywords: continuous fuzzy subsets
zbMATH Keywords: maximal ideals
zbMATH Keywords: product
zbMATH Keywords: joint observable
reviewed by: C. S. Hoo
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6353
OpenAlex ID: W1971635063
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DOI: 10.1006/JMAA.1999.6353
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description: scientific article; zbMATH DE number 1309055