Results of Certain Local Cohomology Modules

Abstract

Abstract. Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that Ext i R (R/I, H t I,J (M )) is finitely generated for i = 0, 1 where t = inf{i ∈ N 0 : H i I,J (M ) is not finitely generated}. Also, we prove that H i I+J (H t I,J (M )) is Artinian when dim(R/I + J) = 0 and i = 0, 1.