Strict MV-algebras
type: Item
instance of: scholarly article
title: Strict MV-algebras
zbMATH Open document ID: 0936.06011
author: Rosanna Ambrosio
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-05T00:00:00Z
review text: The aim of this paper is to go deeper into the questions of MV-algebras provided with square roots. Höhle proposed a classification of MV-algebras with square roots, introducing the strict MV-algebras and proving that every MV-algebra with square roots is exactly a Boolean algebra, or a strict algebra, or isomorphic to the product of both. Due to their important role we propose a characterization of strict MV-algebras proving that the following concepts are equivalent: (i) strict MV-algebras, (ii) 2-atomless MV-algebras. Moreover we show that a strict MV-algebra contains for every \(n \in N\), \(n\geq 0\), cyclic elements of order \(2^{n+1}\) and we find again the result of Höhle that their generated subalgebra is the set of rational dyadic numbers. Then, referring to the homomorphisms between MV-algebras, we prove that the homomorphic image of a strict MV-algebra is still a strict MV-algebra. \(\copyright\) Academic Press.
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 1348151
zbMATH Keywords: MV-algebras provided with square roots
zbMATH Keywords: strict MV-algebras
zbMATH Keywords: 2-atomless MV-algebras
zbMATH Keywords: cyclic elements
zbMATH Keywords: rational dyadic numbers
zbMATH Keywords: homomorphisms
zbMATH Keywords: homomorphic image
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6482
OpenAlex ID: W2003762000
cites work: Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
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DOI: 10.1006/JMAA.1999.6482
description: scientific article; zbMATH DE number 1348151