Top generalized local cohomology modules

Authors: AMIR MAFI

Abstract: Let (R,m) be a commutative Noetherian local ring and M, N two non-zero finitely generated R-modules with d(M)=n<\infty and dim(N)=d. In this paper, we show that if the top generalized local cohomology module H_m^{n+d} (M,N) \neq 0, then the following statements are equivalent: (i) Ann(0:_{H_m^d(N)}p)=p for all p \in Var(Ann(H_m^d(N))); (ii) Ann(0:_{H_m^{n+d}(M,N)}p)=p for all p \in Var (Ann(H_m^{n+d}(M,N))).

Keywords: Artinian module, Generalized local cohomology

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