DEDEKIND COMPLETIONS OF BOUNDED ARCHIMEDEAN ℓ-ALGEBRAS

DOI10.1142/S0219498812501393zbMath1269.06006OpenAlexW2131217542MaRDI QIDQ4904445

Bruce Olberding, Patrick J. Morandi, Guram Bezhanishvili

Publication date: 29 January 2013

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498812501393

zbMATH Keywords

\(C^\ast\)-algebrainjective hullcompact Hausdorff spaceprojective coverBaer ringDedekind completionextremally disconnected spaceuniform completion\(\ell\)-algebraessential closureGelfand-Neumark-Stone duality\(\ell\)-ring

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Real-valued functions in general topology (54C30) Ordered rings, algebras, modules (06F25) Extremally disconnected spaces, (F)-spaces, etc. (54G05) Ordered rings (13J25)

Related Items (6)

Canonical extensions of bounded Archimedean vector lattices ⋮ A unified approach to Gelfand and de Vries dualities ⋮ A point-free approach to canonical extensions of Boolean algebras and bounded Archimedean \(\ell \)-algebras ⋮ A generalization of Gelfand-Naimark-Stone duality to completely regular spaces ⋮ Gelfand-Naimark-Stone duality for normal spaces and insertion theorems ⋮ De Vries powers: a generalization of Boolean powers for compact Hausdorff spaces.

Cites Work

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• The Completion of a Lattice Ordered Group
• Boundedness Properties in Function-Lattices
• Über das System aller stetigen Funktionen auf einem topologischen Raum
• A General Theory of Spectra. I

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