TY - JOUR
AU - Yengui, Ihsen
AU - Ben Amor, Faten
PY - 2021/03/19
Y2 - 2021/04/11
TI - Saturation of finitely-generated submodules of free modules over Prüfer domains
JF - Armenian Journal of Mathematics
JA - Armen.J.Math.
VL - 13
IS - 1
SE - Articles
DO -
UR - http://armjmath.sci.am/index.php/ajm/article/view/497
SP -
AB - <p>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).</p>
ER -