Weak \((\mathfrak{m},\mathfrak{n})\)-distributivity of lattice ordered groups and of generalized MV-algebras
type: Item
instance of: scholarly article
title: Weak \((\mathfrak{m},\mathfrak{n})\)-distributivity of lattice ordered groups and of generalized MV-algebras
zbMATH Open document ID: 1095.06011
published in: Soft Computing
publication date: 2006-03-02T00:00:00Z
review text: For any cardinals \(\mu\) and \(\mu'\), Sikorski defined weak \((\mu,\mu')\)-distributivity in the framework of Boolean algebras. The author investigates this notion in the wider context of GMV-algebras (i.e., the noncommutative generalization of MV-algebras) and of lattice-ordered groups. In particular, he proves that lattice-ordered groups which are weakly \((\mu,\mu')\)-distributive form a radical class. A similar result is proved for GMV-algebras. For background on MV-algebras see the monograph by \textit{R. L. O. Cignoli}, \textit{I. M. L. D'Ottaviano} and \textit{D. Mundici} [Algebraic foundations of many-valued reasoning, Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)].
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 5009507
zbMATH Keywords: lattice-ordered group
zbMATH Keywords: generalized MV-algebra
zbMATH Keywords: radical class
author: Ján Jakubík
reviewed by: Daniele Mundici
MaRDI profile type: Publication
full work available at URL: s00500-004-0433-0
OpenAlex ID: W2579273330
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DOI: 10.1007/S00500-004-0433-0
description: scientific article; zbMATH DE number 5009507