Saturation of finitely-generated submodules of free modules over Prüfer domains

Author(s)

Saturation of finitely-generated submodules of free modules over Prüfer domains IhsenYengui Yengui

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).

DOI: 10.52737/18291163-2021.13.1-1-21 Armenian Journal of Mathematics, 13(1) 1-21

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Keywords

Valuation domains, Echelon form, Saturation, Abelian groups, Prüfer domains

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