Lateral completion and structure sheaf of an Archimedean \(l\)-group
type: Item
instance of: scholarly article
title: Lateral completion and structure sheaf of an Archimedean \(l\)-group
zbMATH Open document ID: 1170.06007
author: Wolfgang Rump
author: Yichuan Yang
published in: Journal of Pure and Applied Algebra
publication date: 2008-11-11T00:00:00Z
review text: The notion of lateral completion of a lattice-ordered group has been investigated by several authors. Let \(\widetilde{G}\) be the structure sheaf of an abelian lattice-ordered group \(G\). The set of all prime \(\ell\)-ideals of \(G\) endowed with the natural topology is denoted by Spec\(^*G\). The authors define \(E(G)\) to be the direct limit \(\varinjlim\Gamma(U,\widetilde{G})\), where \(U\) runs through the dense open subsets of Spec\(^*G\). The main result of the paper consists in proving that if \(G\) is Archimedean then \(E(G)\) coincides with the lateral completion of \(G\). This result is then applied for constructing the essential closure of \(G\).
reviewed by: Ján Jakubík
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 5364862
zbMATH Keywords: Archimedean lattice-ordered group
zbMATH Keywords: lateral completion
zbMATH Keywords: structure sheaf
zbMATH Keywords: prime \(\ell\)-ideal
zbMATH Keywords: essential closure
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.05.013
OpenAlex ID: W2009380224
cites work: Q5752627
cites work: Q4039742
cites work: Convergence and Cauchy Structures on Lattice Ordered Groups
cites work: The Generalized Orthocompletion and Strongly Projectable Hull of a Lattice Ordered Group
cites work: Unique Representation of Archimedean Lattice Groups and Normal Archimedean Lattice Rings
cites work: Lateral completion for arbitrary lattice groups
cites work: The lateral completion of an arbitrary lattice group
cites work: Lateral and Dedekind Completion of Archimedean Lattice Groups
cites work: Groupes et anneaux reticules
cites work: Q5507659
cites work: A characterization of lattice-ordered groups by their convex L-subgroups
cites work: The Lateral Completion of a Lattice-Ordered Group
cites work: The essential closure of an Archimedean lattice-ordered group
cites work: Q4317872
cites work: Q3929784
cites work: Pseudo-complements in semi-lattices
cites work: Q4266133
cites work: Projective topological spaces
cites work: Q4143433
cites work: Prime Ideal Structure in Commutative Rings
cites work: Q3965241
cites work: Q5638369
cites work: The lateral completion of an arbitrary lattice-ordered group (Bernau's proof revisited)
cites work: The absolute of a topological space and its application to Abelian \(l\)-groups
cites work: Jaffard-Ohm correspondence and Hochster duality
DOI: 10.1016/J.JPAA.2008.05.013
Recommended article: Sheaves of abelian \(l\)-groups
Recommended article: The structure of a complete $l$-group
Recommended article: Epicomplete Archimedean l-Groups and Vector Lattices
Recommended article: Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit
Recommended article: Q4336223
Recommended article: Completions of Grothendieck groups
Recommended article: More on the laterally \(\sigma\)-complete reflection of an Archimedean lattice-ordered group
Recommended article: Lateral and Dedekind completions of strongly projectable lattice ordered groups
Recommended article: Completion of \(L\)-topological groups
Recommended article: On a relative uniform completion of an archimedean lattice ordered group
description: scientific article; zbMATH DE number 5364862