Boolean products of BL-algebras
type: Item
instance of: scholarly article
title: Boolean products of BL-algebras
zbMATH Open document ID: 0966.03055
author: Antonio Di Nola
author: George Georgescu
author: Laurenţiu Leuştean
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-07-26T00:00:00Z
review text: BL algebras are the Lindenbaum algebras of Hájek's Basic Logic. As shown in \textit{P. Hájek}'s book [Metamathematics of fuzzy logic, Kluwer, Dordrecht, Trends in Logic, Studia Logica Library, Vol. 4 (1998; Zbl 0937.03030)], BL algebras generalize Chang's MV-algebras, symmetric Heyting algebras, and product algebras. They capture precisely those equational properties that are valid for all continuous ``triangular norms'' and their adjoint implications. The authors characterize Boolean products of BL-chains, weak Boolean products of local BL-algebras, and of perfect BL-algebras.
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 1545038
zbMATH Keywords: BL algebras
zbMATH Keywords: Lindenbaum algebras of Hájek's Basic Logic
zbMATH Keywords: Boolean products of BL-chains
zbMATH Keywords: weak Boolean products
zbMATH Keywords: local BL-algebras
zbMATH Keywords: perfect BL-algebras
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7024
OpenAlex ID: W2035242660
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DOI: 10.1006/JMAA.2000.7024
description: scientific article; zbMATH DE number 1545038