ON THE REPRESENTATION OF SIMPLE RIESZ GROUPS. E. Pardo ∗ Departament de Matemtiques Universitat Aut` onoma de Barcelona 08193 Bellaterra (Barcelona), Spain e-mail address: epardo@mat.uab.es Dedicat al Francesc i la Montse. 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. Introduction In [5], Effros, Handelman and Shen gave one of the most important results in the theory of ordered groups: the Theorem of structure of dimension groups. This Theorem characterizes these groups as direct limits of direct systems of * Partially supported by DGICYT grants no. PB-93-0900 and PB-95-0626, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. This paper is part of the author’s Ph. D. Thesis, written under the supervision of Professor P. Ara.