On the Annihilators of Local Cohomology Modules

Abstract

Let R be a commutative Noetherian ring with nonzero identity, 𝔟a and 𝔟b ideals of R with 𝔟b ⊆ 𝔟a , and M a finitely generated R-module. In this article, for a non-negative integer n, we show that where is the jth local cohomology module of M with respect to 𝔟b . This implies that there exists a positive integer ℓ, depending on M and 𝔟b , such that for all i < f 𝔟b (M) and all ideals 𝔟a of R with 𝔟b ⊆ 𝔟a where f 𝔟b (M) is the finiteness dimension of M relative to 𝔟b . Also, we obtain a new characterization of the concept of M-grade of an ideal of R.