"COFINITENESS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES"

Abstract

"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases."