English

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Rings and Algebras 2011-11-01 v1 Functional Analysis K-Theory and Homology Operator Algebras

Abstract

It is shown that, for any field F \subseteq R, any ordered vector space structure of F^n with Riesz interpolation is given by an inductive limit of sequence with finite stages (F^n,\F_{>= 0}^n) (where n does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with F replaced by the integers, Z. Indeed, it shows that although Effros and Shen's conjecture is false, it is true after tensoring with Q.

Keywords

Cite

@article{arxiv.1110.6851,
  title  = {Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture},
  author = {Aaron Tikuisis},
  journal= {arXiv preprint arXiv:1110.6851},
  year   = {2011}
}

Comments

11 pages

R2 v1 2026-06-21T19:28:31.988Z