Rational polyhedra and projective lattice-ordered abelian groups with order unit
type: Item
instance of: scholarly article
zbMATH Open document ID: 1275.06002
DOI: 10.1142/S0219199712500174
author: Daniele Mundici
author: Leonardo Manuel Cabrer
published in: Communications in Contemporary Mathematics
publication date: 2012-08-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/0907.3064
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 08B30
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 54D05
zbMATH DE Number: 6072527
zbMATH Keywords: lattice-ordered abelian group
zbMATH Keywords: strong order unit
zbMATH Keywords: rational polyhedron
zbMATH Keywords: regular fan
zbMATH Keywords: desingularization
zbMATH Keywords: contractibility
zbMATH Keywords: collapsibility MV-algebra
zbMATH Keywords: Whitehead theorem
zbMATH Keywords: weak Oda conjecture
MaRDI profile type: Publication
arXiv ID: 0907.3064
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OpenAlex ID: W2962782932
title: Rational polyhedra and projective lattice-ordered abelian groups with order unit
review text: The paper is devoted to characterizing the finitely generated projectives in the category \(U\) of unital lattice-ordered groups (\(\ell\)-groups), i.e., \(\ell\)-groups with distinguished order unit. The authors solve this problem and show that it is much more complicated than the corresponding problem for \(\ell\)-groups. In fact, in the paper it is shown that various arithmetical, geometric and topological conditions must be imposed to ensure that a finitely presented unital \(\ell\)-group is projectable in \(U\).
reviewed by: Jiří Rachůnek
description: scientific article; zbMATH DE number 6072527