Some Remarks on The Weak Integral Closure of a Filtration Relative to a Module

Authors

  • Farhad Dorostkar Guilan university

Keywords:

The weak integral closure of a filtration, the asymptotic prime divisors of a filtration, the weak integral closure of a filtration relative to a module, the asymptotic prime divisors of a filtration relative to a module.

Abstract

In this paper, we will see some new results about  the weak integral closureof a filtration relative to a module and  the asymptotic prime divisors of a filtration relative to a module. Especially, we obtain some new results for the weak integral closureof a filtration relative to an injective module.For example,   if $f = \{I_{n}\}_{n \geq 0} $ is aNoetherian filtration on a Noetherian ring $R$ and  $E$ is an injective $R-$module then it is shown that  the asymptotic prime divisors of a filtration $f$ relative to $E$  can be characterized by the asymptotic prime divisors of the filtration $f$ and also it is shown that  the sequence $(Ass (R/Clos_R(f^{(n)}, E))))_{n\in \mathbb{N} }$  is ultimately constant.

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Published

2025-08-18

Issue

Vol. 19

Section

Vol. 19, No. 4, (2025)

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