On the localic Yosida representation of an archimedean lattice ordered group with weak order unit
type: Item
instance of: scholarly article
title: On the localic Yosida representation of an archimedean lattice ordered group with weak order unit
zbMATH Open document ID: 0732.06009
DOI: 10.1016/0022-4049(91)90004-L
author: Richard N. Ball
author: Anthony W. Hager
published in: Journal of Pure and Applied Algebra
publication date: 1991-01-01T00:00:00Z
review text: This paper is best viewed as an extension of work of \textit{J. Madden} [Frames associated with an Abelian \(\ell\)-group, Trans. Am. Math. Soc. (to appear)] and \textit{J. Madden} and \textit{J. Vermeer} [J. Pure Appl. Algebra 68, No.1/2, 243-252 (1990; Zbl 0718.06005)]. What is new here is a proof of the functoriality of the Yosida representation, by which is meant the adjointness of the functors which connect W, the category of Archimedean lattice ordered groups with weak order unit, with the category F of frames. From the introduction: ``But a more fundamental point of departure of this article from Madden's, and perhaps its main value to a reader, is that the methods we use are extremely direct and computational, and give a kind of primer on the subject of CL and of the localic Yosida representation which affords deep insight into W.''
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 4210210
zbMATH Keywords: category of frames
zbMATH Keywords: locales
zbMATH Keywords: functoriality of the Yosida representation
zbMATH Keywords: category of Archimedean lattice ordered groups with weak order unit
zbMATH Keywords: localic Yosida representation
reviewed by: Spencer P. Hurd
MaRDI profile type: Publication
cites work: Convex vector lattices and l-algebras
cites work: Q3813848
cites work: Q3496379
cites work: Epicomplete Archimedean l-Groups and Vector Lattices
cites work: Q3490607
cites work: Groupes et anneaux reticules
cites work: Q4724682
cites work: Q4161373
cites work: Residue class fields of lattice-ordered algebras
cites work: Q5682456
cites work: Atomless Parts of Spaces.
cites work: Q3711309
cites work: Q5638775
cites work: Q3480884
cites work: Frames Associated with an Abelian l-Group
cites work: \(\kappa\)-frames
cites work: Lindelöf locales and realcompactness
cites work: Epicomplete archimedean l-groups via a localic Yosida theorem
cites work: On the representation of the vector lattice
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description: scientific article; zbMATH DE number 4210210