A short note on annihilators of local cohomology modules

摘要

Let R be a commutative Noetherian domain, a nonzero R-module of finite injective dimension, and I be a nonzero ideal of R. In this paper, we prove that whenever injdimM = cd(I, M) = t, then the annihilator of H-I(t)(M) is zero. Also, we calculate the annihilator of H-I(n+t) (N, M) for finitely generated R-modules N and 51 with conditions projdimN = n < infinity and injdimM = t < infinity. Moreover, if (R, m) is a regular Noetherian local ring and p is an element of Spec(R) such that d = dimR/p >= 2, then we show that there exists an ideal J of R such that p subset of J, htJ/p =1 and J(n) H-m(1) (R/p(n)) = 0.