Annihilators and attached primes of local cohomology modules with respect to a system of ideals

Document Type: Research Paper

Author

Department of Natural Science Education, Dong Nai University, Bien Hoa city, Dong Nai province, Vietnam.

10.29252/as.2020.1959

Abstract

Let $\Phi$ be a system of ideals of a commutative Noetherian ring, we study the annihilators and attached primes of local cohomology modules with respect to a system of ideals.  We prove that if $M$ is a non-zero finitely generated $R$-module of finite dimension $d$ and $\Phi$ is a system of ideals, then$$Att(H^d_\Phi(M))=\{p\in Ass M\mid cd(\Phi,R/p)=d\}.$$ Moreover, if the cohomology dimension of $M$ with respect to $\Phi$ is $dim M-1,$ then $$Att(H^{dim M-1}_\Phi(M))=\{p\in Supp M \mid cd(\Phi,R/p)=\dim M-1\}.$$

Keywords


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