Some comments and examples on generation of (hyper-)Archimedean \(\ell\)-groups and \(f\)-rings
type: Item
instance of: scholarly article
title: Some comments and examples on generation of (hyper-)Archimedean \(\ell\)-groups and \(f\)-rings
zbMATH Open document ID: 1228.06008
author: Anthony W. Hager
author: Donald G. Johnson
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2010-10-12T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/115904
review text: It is important to know the theory of subcategories with the objects that are obtained by adjoining a special element to the original objects. For instance, Mundici's equivalence also holds between the categories of abelian \(\ell\)-groups and perfect MV-algebras, which is due to the fact that for an abelian \(\ell\)-group \(G\), the lexicographical product of \(G\) and \(\mathbb Z\) admits a strong order unit. The paper under review discusses the process of adjoining a weak order unit to an \(\ell\)-group, or an identity to an \(f\)-ring, and finds significant contrasts between these cases. In \(\ell\)-groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures they generate, as illustrated by a basic example of Conrad and Martinez. For reduced \(f\)-rings, on the other hand, these properties do inherit upwards.
reviewed by: Yichuan Yang
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 5799082
zbMATH Keywords: hyperarchimedean \(\ell \)-groups
zbMATH Keywords: \(f\)-rings
zbMATH Keywords: Archimedean \(\ell\)-groups
zbMATH Keywords: weak order unit
MaRDI profile type: Publication
OpenAlex ID: W2329451300
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DOI: 10.5802/AFST.1276
description: scientific article; zbMATH DE number 5799082