Calcul matriciel généralisé sur les domaines de Prüfer

Abstract

In this paper, we first present an algorithm for computing the Hermite normal form of pseudo-matrices over Prüfer domains. This algorithm allows us to provide constructive proofs of the main theoretical results on finitely presented modules over Prüfer 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 Prüfer domains of dimension one about the Smith normal form.

arXiv commentin French