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

Armenian Journal of Mathematics

View Publication Info
 
 
Field Value
 
Title Saturation of finitely-generated submodules of free modules over Prüfer domains
 
Creator Yengui, Ihsen
Ben Amor, Faten
 
Subject Valuation domains
Prüfer domains
Echelon form
Saturation
Abelian groups
13C99
13P99
20K10
20K15
 
Description 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).
 
Publisher National Academy of Sciences of Armenia
 
Date 2021-03-19
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
 
Format application/pdf
 
Identifier http://armjmath.sci.am/index.php/ajm/article/view/497
 
Source Armenian Journal of Mathematics; Vol. 13 No. 1 (2021): Saturation of finitely-generated submodules of free modules over Prüfer domains
1829-1163
 
Language eng
 
Relation http://armjmath.sci.am/index.php/ajm/article/view/497/166
 
Rights Copyright (c) 2021 Armenian Journal of Mathematics
http://creativecommons.org/licenses/by/4.0
 

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