Simple Riesz groups having wild intervals

Details Simple Riesz groups having wild intervals Simple Riesz groups having wild intervals

2004-05-03

arxiv.org/abs/math/0405035v1

Mathematics

Operator Algebras

27 pages

Scientific paper

We prove that every partially ordered simple group of rank one which is not Riesz embeds into a simple Riesz group of rank one if and only if it is not isomorphic to the additive group of the rationals. Using this result, we construct examples of simple Riesz groups of rank one $G$, containing unbounded intervals $(D_n)_{n\geq 1}$ and $D$, that satisfy: (a) For each $n\geq 1$, $tD_n\ne G^+$ for every $t< q_n$, but $q_nD_n=G^+$ (where $(q_n)$ is a sequence of relatively prime integers); (b) For every $n\geq 1$, $nD\ne G^+$. We sketch some potential applications of these results in the context of K-Theory.

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