On the radical of the annihilators of local cohomology modules

Abstract

Let R be a noetherian ring, M a non-zero nitely generated R-module of dimension d. Let cd(a;M) = d. In this paper we calculate the rad-ical of the annihilator of the top local cohomology module Hda(M). In fact, we prove that there exists a submodule S_R(a;M) of M such that √Ann_R(H^d_a(M)) = Ann_R(M/S_R(a;M)). By using this result we show that for a complete local ring(R;m) we have Att_R(H^d_a(M)) = Min Supp_R(M/S_R(a;M)).