Generalized matrix calculation on domains from Prufer

In this paper, we first present an algorithm for computing the Hermite normal form of pseudo-matrices over Prilfer domains. This algorithm allows us to provide constructive proofs of the main theoretical results on finitely presented modules over Prufer 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 Prufer domains of dimension one about the Smith normal form. (C) 2019 Elsevier Masson SAS. Tous droits reserves.