The closed subgroup problem for lattice-ordered groups
type: Item
instance of: scholarly article
title: The closed subgroup problem for lattice-ordered groups
zbMATH Open document ID: 0682.06011
DOI: 10.1007/BF01188514
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Kenoyer gave two examples proving that in the lattice of convex \(\ell\)- subgroups of a lattice-ordered group it was impossible to distinguish the closed convex \(\ell\)-subgroups. However, one of his examples was non- normal-valued. Here the same question is recast for normal-valued \(\ell\)- groups, and it remains open. The main theorem gives an interesting class of \(\ell\)-groups in which closed convex \(\ell\)-subgroups can be recognized in the lattice of convex \(\ell\)-subgroups.
Mathematics Subject Classification ID: 06F15
zbMATH DE Number: 4116602
zbMATH Keywords: lattice-ordered group
zbMATH Keywords: normal-valued l-groups
zbMATH Keywords: closed convex l-subgroups
zbMATH Keywords: lattice of convex l-subgroups
author: Jorge Martinez
reviewed by: Javier Martínez-Martínez
MaRDI profile type: Publication
cites work: Q4148027
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full work available at URL: https://doi.org/10.1007/bf01188514
OpenAlex ID: W2029028516
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description: scientific article; zbMATH DE number 4116602