Estructura de Grupos Abelianos Ordenados

Abstract

The purpose of this paper is to describe the structure of ordered abelian groups of finite rank, besides being able to be considered as an indispensable bibliographical reference in the field of the classification of ordered abelian groups. This paper compiles, reproducing in an original, detailed, deep and strategic way, all results related to the classification of ordered abelian groups, which are necessary to describe the structure of these groups. This is achieved by establishing until the Hahn’s embedding theorem (Theorem 5.3). This compilation has all my proofs of own results, and of others that were provided, but above all, proposed by Ribenboim in [20] and Ugarte in [23]. Between these, the result that fulfills the purpose, the Hahn’s embedding theorem for the case of ordered abelian groups of finite rank (Theorem 5.8). In this manner, an almost complete description of the theory of divisible and ordered abelian groups is achieved.