Attached and Assoiciated Primes Of Local Cohomology Modules Via Linkage

TL;DR

This paper investigates the properties of local cohomology modules over a Noetherian ring, focusing on associated primes, cofiniteness, and Artinianness in the context of linked ideals over modules.

Contribution

It introduces a new concept of linkage of ideals over modules and explores its impact on local cohomology modules' properties.

Findings

Characterization of associated primes of local cohomology modules

Conditions for cofiniteness and Artinianness in linked ideal contexts

Extension of linkage theory to local cohomology modules

Abstract

Let $R$ be a commutative Noetherian ring and $M$ be a finitely generated $R$-module. Considering the new concept of linkage of ideals over a module, we study associated prime ideals, cofiniteness and Artinianness of local cohomology modules of $M$ with respect to some linked ideals over it.