Order completions of Archimedean Riesz spaces and \(\ell\)-groups
type: Item
instance of: scholarly article
title: Order completions of Archimedean Riesz spaces and \(\ell\)-groups
zbMATH Open document ID: 0548.06008
DOI: 10.1007/BF01190426
author: Eric Langford
author: Charalambos D. Aliprantis
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: Every Archimedean Riesz space (vector lattice) has a Dedekind completion that is essentially unique. Since the Dedekind completion has certain other nice properties (e.g. the projection property) and is easily shown to be universal in the category of Dedekind complete objects and appropriate morphisms, the existence of other completions can be demonstrated by general category theory.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 3873397
zbMATH Keywords: Archimedean Riesz space
zbMATH Keywords: Dedekind completion
zbMATH Keywords: category of Dedekind complete objects
reviewed by: A. M. W. Glass
MaRDI profile type: Publication
cites work: Almost σ-Dedekind Complete Riesz Spaces and the Main Inclusion Theorem
cites work: Q5822256
cites work: The lateral completion of an arbitrary lattice group
cites work: Lateral and Dedekind Completion of Archimedean Lattice Groups
cites work: On certain completions of K-lineals
cites work: The Lateral Completion of a Lattice-Ordered Group
cites work: The hulls of representablel-groups andf-rings
cites work: Inextensible Riesz spaces
cites work: Some Characterizations of The Projection Property in Archimedean Riesz Spaces
cites work: Intermediate Riesz spaces
cites work: On a new construction of Dedekind completion of vector lattices and of l- groups with division
cites work: Order completeness and disjoint completeness of linear partially ordered spaces
full work available at URL: https://doi.org/10.1007/bf01190426
OpenAlex ID: W2063393280
description: scientific article; zbMATH DE number 3873397