Amir Mafi

Let a  b be two ideals of commutative Noetherian ring R and A an Artinian R-module. For a non-negative integer n, we show that up+q=n Ann(Torq p(R=b;Ha q (A)))  Ann(TorR n (R=b;A)): As an immediate consequence, if Ha i (A) is Artinian for all i < n then a  Rad(Ann(Hb i (A))) for all i < n. Moreover, we prove that if a = (x1; : : : ; xn) and c = \t1 \n i=0 Ann(TorR i (R=at;A)), then ck  \n􀀀1 i=0 Ann(Ha i (A)) where k = (n [ n2 ]).