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Real Dimension Groups

Published online by Cambridge University Press:  20 November 2018

David Handelman
David Handelman*
Affiliation:
Mathematics Department, University of Ottawa, Ottawa ON K1N 6N5 e-mail: dehsg@uottawa.ca
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Abstract

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Dimension groups (not countable) that are also real ordered vector spaces can be obtained as direct limits (over directed sets) of simplicial real vector spaces (finite dimensional vector spaces with the coordinatewise ordering), but the directed set is not as interesting as one would like; for instance, it is not true that a countable-dimensional real vector space that has interpolation can be represented as such a direct limit over a countable directed set. It turns out this is the case when the group is additionally simple, and it is shown that the latter have an ordered tensor product decomposition. In an appendix, we provide a huge class of polynomial rings that, with a pointwise ordering, are shown to satisfy interpolation, extending a result outlined by Fuchs.

Keywords

46A4006F2013J2519K14dimension groupsimplicial vector spacedirect limitRiesz interpolation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 551 - 563
Copyright
Copyright © Canadian Mathematical Society 2013

References

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