Convergence in perfect MV-algebras
type: Item
instance of: scholarly article
title: Convergence in perfect MV-algebras
zbMATH Open document ID: 0920.06005
author: George Georgescu
author: Ioana Leuştean
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-13T00:00:00Z
review text: MV-algebras are the Lindenbaum algebras of the infinite-valued calculus of Łukasiewicz. In an earlier paper the authors investigated general order-convergence properties in MV-algebras, using the categorical equivalence \(\Gamma\) between MV-algebras and abelian lattice-ordered groups with strong unit [see \textit{D. Mundici}, ``Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus'', J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)]. In the present paper the authors focus their attention on the subclass of perfect MV-algebras. After defining the appropriate notion of Cauchy completion, they establish its existence and uniqueness.
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 1246339
zbMATH Keywords: Cauchy MV-sequence
zbMATH Keywords: order-convergence
zbMATH Keywords: perfect MV-algebras
zbMATH Keywords: Cauchy completion
reviewed by: Daniele Mundici
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6119
OpenAlex ID: W2078124821
cites work: Semi-simple and complete MV-algebras
cites work: Local MV-algebras
cites work: Yosida Type Representation for Perfect MV‐Algebras
cites work: Groupes et anneaux reticules
cites work: Q5331549
cites work: Algebraic Analysis of Many Valued Logics
cites work: A New Proof of the Completeness of the Lukasiewicz Axioms
cites work: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
cites work: Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions
cites work: Perfect MV-algebras are categorically equivalent to Abelian \(l\)-groups
cites work: Q4347371
cites work: Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
DOI: 10.1006/JMAA.1998.6119
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description: scientific article; zbMATH DE number 1246339