Calcul matriciel g\'en\'eralis\'e sur les domaines de Pr\"ufer

Abstract

In this paper, we first present an algorithm for computing the Hermite normal form of pseudo-matrices over Pr\"ufer domains. This algorithm allows us to provide constructive proofs of the main theoretical results on finitely presented modules over Pr\"ufer domains and to discuss the resolution of linear systems. In some sense, we generalize the methodology developed by Henri Cohen for Dedekind domains. Finally, we present some results over Pr\"ufer domains of dimension one about the Smith normal form.