Integral closure of a filtration relative to a Noetherian module

Document Type : Research Paper

Authors

Department of Pure Mathematics, University of Guilan, Rasht, Iran

Abstract

Let

M

be a Noetherian

R -

module.
In this paper we will introduce the integral closure of a filtration

F = {I_{n}}_{n \geq 0}

relative to the Noetherian module

M

and prove some related results.\
The integral closure of a filtration

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

\tilde{F} = {{\tilde{I}}_{n}}_{n \geq 0}

, where

{\tilde{I}}_{n}

is the image of

I_{n}

under the natural ring homomorphism

R \to R / (A n n_{R} (M))

for every

n \geq 0

Keywords