A simple proof of uniqueness for torsion modules over P.I.D.’s

Abstract

The aim of this paper is to glve an alternative proof of uniqueness for the decomposition of a flnitely generated torsión module over a P.I.D.(= principal ideal domain) as a direct sum of indecomposable submodules. Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces. For the sake of completeness we also inelude a proof of the existence theorem.