One chain generated varieties of MV-algebras
type: Item
instance of: scholarly article
title: One chain generated varieties of MV-algebras
zbMATH Open document ID: 0949.06004
published in: Journal of Algebra
publication date: 2000-06-07T00:00:00Z
review text: In his paper ``Free products in the category of abelian \(l\)-groups with strong unit'' [J. Algebra 113, No. 1, 89-109 (1988; Zbl 0658.06010)], the present reviewer established the amalgamation property for the variety of Chang's MV-algebras. The latter are the Lindenbaum algebras of the infinite-valued Łukasiewicz logic and are deeply related to abelian lattice-orderd groups and also to AF \(C^*\)-algebras. For a comprehensive account see the monograph of \textit{R. Cignoli, I. M. L. D'Ottaviano} and \textit{D. Mundici} [Algebraic foundations of many-valued reasoning (Trends in Logic -- Studia Logica Library 7, Kluwer, Dordrecht) (2000; Zbl 0937.06009)]. Komori gave a complete classification of the subvarieties of MV-algebras. In the present paper, the authors prove that a subvariety has the amalgamation property iff it is generated by precisely one MV-chain. They also introduce a notion of ``abstract conditional space'', proving its equivalence with the notion of Post algebra of order 2.
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06B20
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06D25
zbMATH DE Number: 1429463
zbMATH Keywords: conditional
zbMATH Keywords: abstract conditional space
zbMATH Keywords: amalgamation
zbMATH Keywords: MV-algebras
zbMATH Keywords: subvariety
zbMATH Keywords: MV-chain
zbMATH Keywords: Post algebra
author: Antonio Di Nola
author: Ada Lettieri
MaRDI profile type: Publication
full work available at URL: jabr.1999.8136
OpenAlex ID: W2093069338
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DOI: 10.1006/JABR.1999.8136
description: scientific article; zbMATH DE number 1429463