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

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

2011-10-31

arxiv.org/abs/1110.6851v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

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.

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