A characterisation of lattice-ordered Abelian groups
type: Item
instance of: scholarly article
title: A characterisation of lattice-ordered Abelian groups
zbMATH Open document ID: 0789.06011
DOI: 10.1007/BF03025717
author: Daniele Mundici
author: George A. Elliott
published in: Mathematische Zeitschrift
publication date: 1994-06-06T00:00:00Z
full work available at URL: https://eudml.org/doc/174525
review text: It is pointed out that it is possible to define the prime ideal spectrum of any ordered Abelian group with distributive ideal lattice, and that this provides a point of contrast between the Riesz interpolation property, which (at least in the case of a countable group) does not impinge on the spectrum, and the lattice property, which -- in the presence of the interpolation property, and the well-known local property that prime quotients are totally ordered -- is determined by the spectrum. (The determining property is that the intersection of two compact open subsets is compact).
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 549767
zbMATH Keywords: prime ideal spectrum
zbMATH Keywords: ordered Abelian group
zbMATH Keywords: distributive ideal lattice
zbMATH Keywords: Riesz interpolation property
zbMATH Keywords: lattice property
reviewed by: George A. Elliott
MaRDI profile type: Publication
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OpenAlex ID: W1988684505
description: scientific article; zbMATH DE number 549767