University of Guilan Journal of Algebra and Related Topics 2345-3931 10 1 2022 06 20 Integral closure of a filtration relative to a Noetherian module 129 141 5621 10.22124/jart.2021.20320.1302 EN F. Dorostkar Department of Pure Mathematics, University of Guilan, Rasht, Iran M. Yahyapour-Dakhel Department of Pure Mathematics, University of Guilan, Rasht, Iran Journal Article 2021 08 07  Let  $M$ be a Noetherian $R-$module.<br />In this paper we will introduce the integral closure of a filtration ${\mathcal{F}}=\{I_{n}\}_{n\geq 0}$  relative to the Noetherian module  $M$ and prove some related results.\\<br /> The integral closure of a filtration ${\mathcal{F}}=\{I_{n}\}_{n\geq 0}$  relative to $M$  is a filtration and it has an interesting relationship with  the integral closure of the filtration<br /> ${\widetilde{\mathcal{F}}}=\{\widetilde{I}_{n}\}_{n\geq 0}$, where $\widetilde{I}_{n}$ is the image of $I_n$  under the natural ring homomorphism  $R\rightarrow R/(Ann_R(M))$ for every $n\geq 0$. https://jart.guilan.ac.ir/article_5621_670999f57a2e5182656b4bc47f990dba.pdf