A short note on annihilators of local cohomology modules

Abstract

Let [Formula: see text] be a commutative Noetherian domain, [Formula: see text] a nonzero [Formula: see text]-module of finite injective dimension, and [Formula: see text] be a nonzero ideal of [Formula: see text]. In this paper, we prove that whenever [Formula: see text], then the annihilator of [Formula: see text] is zero. Also, we calculate the annihilator of [Formula: see text] for finitely generated [Formula: see text]-modules [Formula: see text] and [Formula: see text] with conditions [Formula: see text] and [Formula: see text]. Moreover, if [Formula: see text] is a regular Noetherian local ring and [Formula: see text] such that [Formula: see text], then we show that there exists an ideal [Formula: see text] of [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text].