Some Properties of Generalized Local Cohomology Modules
نویسنده
چکیده
Let R be a commutative Noetherian ring, a an ideal of R, M and N be two finitely generated R-modules. Let t be a positive integer. We prove that if R is local with maximal ideal m and M ⊗R N is of finite length then H t m (M, N) is of finite length for all t ≥ 0 and lR(H t m (M, N)) ≤ ∑t i=0 lR(Ext i R (M, H m (N))). This yields, lR(H t m (M, N)) = lR(Ext t R(M, N)). Additionally, we show that Ext R (R/a, N) is Artinian for all i ≤ t if and only if H a (M, N) is Artinian for all i ≤ t. Moreover, we show that whenever dim(R/a) = 0 then H a (M, N) is Artinian for all t ≥ 0.
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