Abstract
Let (R, ) 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 (M,N) = 0, then the following statements are equivalent: (i) Ann(0 :Hd m(N) ) = for all ∈ Var(Ann(H d (N))) ; (ii) Ann(0 : Hn+d m (M,N) ) = for all ∈ Var(Ann(H (M,N))) .
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