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

Armenian Journal of Mathematics

article

Ihsen Yengui¹  Faten Ben Amor¹ 

[1] Université de Sfax

关键词: Valuation domains;    Pr¨ufer domains;    Echelon form;    Saturation;    Abelian groups;   

DOI  :  10.52737/18291163-2021.13.1-1-21

学科分类：环境科学（综合）

来源: National Academy of Sciences of the Republic of Armenia

【 摘 要 】

We propose to give an algorithm for computing the R-saturation of a finitely-generated submodule of a free module E over a Pr¨ufer 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 Pr¨ufer 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 B´ezout domain. Particular attention is paid to the case where R is a principal ideal domain (Z as the main example).

【 授权许可】

CC BY