Singular Archimedean lattice-ordered groups
type: Item
instance of: scholarly article
title: Singular Archimedean lattice-ordered groups
zbMATH Open document ID: 0936.06015
author: Anthony W. Hager
author: Jorge Martinez
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: The paper deals with the category \(W\) of all archimedean lattice-ordered groups (\(l\)-groups) with a designated weak unit and its full subcategory \(W_s\) of those \(l\)-groups in which the designated weak unit is singular. The authors also develop a necessary background in category theory concerning extension functors and contracting completion operators. Using this technique, they, for example, prove that the projectable hull in \(W_s\) is a monoreflection, characterize essential hulls in \(W_s\), describe the maximum monoreflection on \(W_s\) by contracting the corresponding monoreflection on \(W\), and analogously characterize the maximal reflection on \(W_s\).
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18A20
zbMATH DE Number: 1407108
zbMATH Keywords: Archimedean \(l\)-group
zbMATH Keywords: weak unit
zbMATH Keywords: singular element
zbMATH Keywords: monoreflective subcategory
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s000120050086
OpenAlex ID: W2065541448
DOI: 10.1007/S000120050086
description: scientific article; zbMATH DE number 1407108