Integral closure of a filtration relative to a Noetherian module

Let  M be a Noetherian R-module.In this paper we will introduce the integral closure of a filtration {\mathcal{F}}=\{I_{n}\}_{n\geq ۰}  relative to the Noetherian module  M and prove some related results.\\ The integral closure of a filtration {\mathcal{F}}=\{I_{n}\}_{n\geq ۰}  relative to M  is a filtration and it has an interesting relationship with  the integral closure of the filtration {\widetilde{\mathcal{F}}}=\{\widetilde{I}_{n}\}_{n\geq ۰}, 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 ۰.

کلیدواژه ها:

Filtration ، Reduction of a filtration ، Noetherian filtration ، Integral closure of a filtration