Mapping Abelian \(\ell\)-groups with strong unit one-one into MV algebras
type: Item
instance of: scholarly article
title: Mapping Abelian \(\ell\)-groups with strong unit one-one into MV algebras
zbMATH Open document ID: 0579.06016
DOI: 10.1016/0021-8693(86)90015-3
author: Daniele Mundici
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: An Abelian \(\ell\)-group (i.e., lattice-ordered group) G is said to have a strong unit u provided \(u\in G^+\) and to every element \(g\in G\) corresponds a natural number n such that \(g\leq nu\). Abelian \(\ell\)-groups with strong unit are important in the theory of \(C^*\)-algebras. MV- algebras, invented by C. C. Chang, are an algebraic counterpart of the \(\aleph_ 0\)-valued Lukasiewicz sentential calculus. Based on these facts and a remark of Dieudonné to the effect that ''invention of functors is one of the main goals of modern mathematics'', the author constructs an object-injective functor from the category of Abelian \(\ell\)-groups with strong unit to the category of MV-algebras. Further results and applications are announced in a note added in proof.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 03G20
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3926994
zbMATH Keywords: lattice-ordered group
zbMATH Keywords: Abelian \(\ell \)-groups
zbMATH Keywords: strong unit
zbMATH Keywords: MV-algebras
zbMATH Keywords: \(\aleph _ 0\)-valued Lukasiewicz sentential calculus
reviewed by: Sergiu Rudeanu
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90015-3
OpenAlex ID: W2025013387
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description: scientific article; zbMATH DE number 3926994