Tensor products of structures with interpolation

Friedrich Wehrung

Vol. 176 (1996), No. 1, 267–285

DOI: 10.2140/pjm.1996.176.267

Abstract

While it is known that the tensor product of two dimension groups is a dimension group, the corresponding problem for interpolation groups has been open for a while. We solve this problem here, by proving that the tensor product of two interpolation groups may not be an interpolation group, even for directed, torsion-free interpolation groups. We also solve the corresponding problems for refinement monoids (with tensor product of commutative monoids) and for lattice-ordered groups (with tensor product of partially ordered abelian groups).

Mathematical Subject Classification 2000

Primary: 06F20

Secondary: 20F60, 20M14

Milestones

Received: 13 October 1994

Revised: 10 May 1995

Published: 1 November 1996