On the representation of simple Riesz groups

Abstract

In this paper we answer Open Problem 2 of Goodearl's book on partially ordered abelian groups in the case of partially ordered sim- ple groups. As a consequence, we obtain a version of the Theorem of structure of dimension groups in the case of simple Riesz groups. Also, we give a method for constructing torsion-free strictly perforated simple Riesz groups of rank one, and we see that every dense additive subgroup of Q can be obtained using this method.