Tensor products of structures with interpolation
type: Item
instance of: scholarly article
title: Tensor products of structures with interpolation
zbMATH Open document ID: 0865.06010
author: Friedrich Wehrung
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
review text: While it is known that tensor products of dimension groups are dimension groups, the corresponding problem for interpolation groups has been open for a while. In this paper, this problem is solved (negatively), by finding two torsion-free Riesz groups whose tensor product (in the category of partially ordered abelian groups) does not satisfy interpolation. The Riesz groups of this example are obtained by lexicographical product of the rationals by finitely presented, non directed partially ordered abelian groups. Analogous problems for refinement monoids (in the category of commutative monoids) or lattice-ordered abelian groups (in the category of partially ordered abelian groups) are also solved.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 950236
zbMATH Keywords: tensor products
zbMATH Keywords: interpolation groups
zbMATH Keywords: torsion-free Riesz groups
zbMATH Keywords: category of partially ordered abelian groups
zbMATH Keywords: lexicographical product
zbMATH Keywords: refinement monoids
zbMATH Keywords: category of commutative monoids
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.267
OpenAlex ID: W4321855207
DOI: 10.2140/PJM.1996.176.267
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description: scientific article; zbMATH DE number 950236