Armenian Journal of Mathematics, 13(1)
ISSN 1829-1163
2022; 1–21
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Saturation of finitely-generated submodules of free modules over Prüfer domains

IhsenYengui Yengui*, Faten Ben Amor

Received: 2024-12-06 · Published: 2022-08-28

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Originally published in Armenian Journal of Mathematics, 13(1), 2022 — https://doi.org/10.52737/18291163-2021.13.1-1-21.

Original title
Saturation of finitely-generated submodules of free modules over Prüfer domains
Authors
IhsenYengui Yengui, Faten Ben Amor
Source journal
Armenian Journal of Mathematics, 13(1)
Published
2022-08-28
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2021.13.1-1-21

Abstract

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).
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