Saturation of finitely-generated submodules of free modules over Prüfer domains
DOI:
https://doi.org/10.52737/18291163-2021.13.1-1-21Keywords:
Valuation domains, Echelon form, Saturation, Abelian groups, Prüfer domainsAbstract
We propose to give an algorithm for computing the $R$-saturation of a finitely-generated submodule of a free module $E$ over a Prüfer domain $R$. To do this, we start with the local case, that is, the case where $R$ is a valuation domain. After that, we consider the global case ($R$ 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 $E=R[X]^m$ 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 $R$ is a Bézout domain. Particular attention is paid to the case where $R$ is a principal ideal domain ($\mathbb{Z}$ as the main example).
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- 2022-08-28 (3)
- 2021-03-19 (1)
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