Annihilators and attached primes of top general local cohomology modules

Faramarzi, Seadat Ollah; Valadbeigi, Hadis

doi:10.22060/ajmc.2025.23121.1230

Annihilators and attached primes of top general local cohomology modules

Articles in Press

Document Type : Original Article

Authors

Seadat ollah Faramarzi

Hadis valadbeigi

Department of Mathematics, Payame Noor University(PNU), Tehran, Iran

10.22060/ajmc.2025.23121.1230

Abstract

Let $\mathrm{R}$ be a commutative Noetherian local ring, $\mathrm{M}$ be a non-zero finitely generated $\mathrm{R}$-module of dimension $d$ and $\Phi$ be a system of ideals of $\mathrm R$. For each $i>d,$ $\large H_{ \Phi}^i (M)$ is zero and $\large H_{ \Phi}^d (M)$ is Artinian. In this paper, we determine the annihilator and the set of attached prime ideals of top general local cohomology module $\large H_{ \Phi}^d (M).$

Keywords

Annihilators

Attached primes

$\mathrm{cd}$-filtration

System of ideals

Subjects