This work is licensed under Creative Commons Attribution–NonCommercial International License
(CC BY-NC 4.0).
We propose to give an algorithm for computing the RR-saturation of a finitely-generated submodule of a free module EE over a Prüfer domain RR. To do this, we start with the local case, that is, the case where RR is a valuation domain. After that, we consider the global case (RR is a Prüfer domain) using the dynamical method. The proposed algorithm is based on an algorithm given by Ducos, Monceur and Yengui in the case E=R[X]mE=R[X]m which is reformulated here in a more general setting in order to reach a wider audience. The last section is devoted to the case where RR is a Bézout domain. Particular attention is paid to the case where RR is a principal ideal domain (ZZ as the main example).