On the annihilators and attached primes of top local cohomology modules

摘要

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that AnnR(H_a~(dimM) (M)) = AnnR(M/T_R(a,M)), where T_R(a,M) is the largest submodule of M such that cd(a, T_R(a,M)) < cd(a,M). Several applications of this result are given. Among other things, it is shown that there exists an ideal b of R such that AnnR(H_a~(dimM) (M)) = AnnR(M/H_b~0(M)). Using this, we show that if H_a~(dimR) (R) = 0, then AttR H_a~(dimR-1) (R) = {p ∈ SpecR| cd(a,R/p) = dimR - 1}. These generalize the main results of Bahmanpour et al. (see [2, Theorem 2.6]), Hellus (see [7, Theorem 2.3]), and Lynch (see [10, Theorem 2.4]).