مشخصات پژوهش

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that AnnR(HdimM a (M)) = AnnR(M/TR(a,M)), where TR(a,M) is the largest submodule of M such that cd(a, TR(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(HdimM a (M)) = AnnR(M/H0b (M)). Using this, we show that if HdimR a (R) = 0, then AttR HdimR−1 a (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]).