Top generalized local cohomology modules

Let (R, m) be a commutative Noetherian local ring and M , N two non-zero finitely generated R- modules with pd(M)= n ∞ and dim(N)= d. In this paper, we show that if the top generalized local cohomology module H n+d m (M, N) ≠ 0, then the following statements are equivalent: (i) Ann(0: H d m (N) p)= p for all p element of Var(Ann(Hd m (N))); (ii) Ann(0: H n+d m (M,N) p)= p for all p element of Var(Ann(Hn+d m (M, N))).