Results on Finiteness of Graded Local Cohomology Modules
نویسنده
چکیده
Let R = ⊕ n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R− module. In this paper we show that if R0 is a local ring of dimension one, then H i R+(H 1 m0R (M)) is Artinian for each i ∈ N0. Let f be the least integer such that H i m0R(M) is not finitely generated graded R−module. In this case, we prove that ΓR+(H i m0R(M)) is Artinian for all i ≤ f . Finally let s be the largest positive integer such that H i m0R(M) is not Artinian. Then we prove that H i m0R (M)/R+H i m0R(M) is Artinian for all i ≥ s. 2000 Mathematics Subject Classification: Primary 13D45, 13E10.
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