Real Dimension Groups

Canadian mathematical bulletin

David Handelman¹ 

[1] Mathematics Department, University of Ottawa, Ottawa ON K1N 6N5

关键词: dimension group;    simplicial vector space;    direct limit;    Riesz interpolation;   

DOI  :  10.4153/CMB-2012-006-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Dimension groups (not countable) that are also real ordered vectorspaces can be obtained as direct limits (over directed sets) ofsimplicial real vector spaces (finite dimensional vector spaces withthe coordinatewise ordering), but the directed set is not asinteresting as one would like, i.e., it is not true that acountable-dimensional real vector space that has interpolation can berepresented as such a direct limit over the a countable directedset. It turns out this is the case when the group is additionallysimple, and it is shown that the latter have an ordered tensor productdecomposition. In the Appendix, we provide a huge class of polynomialrings that, with a pointwise ordering, are shown to satisfyinterpolation, extending a result outlined by Fuchs.

【 授权许可】

Unknown