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Paper IPM / M / 11810  


Abstract:  
e show that if R=⊕_{n ∈ \mathbbN0} R_{n} is a Noetherian homogeneous ring with local base ring (R_{0},\mathfrakm_{0}), irrelevant ideal R_{+}, and M a finitely generated graded Rmodule, then H^{j}_{\mathfrakm0R}(H^{t}_{R+}(M)) is Artinian for j = 0, 1 where t = inf{i ∈ \mathbbN_{0}: H^{i}_{R+}(M)
is not finitely generated}. Also, we prove that if cd(R_{+},M) = 2, then for each i ∈ \mathbbN_{0}, H^{i}_{\mathfrakm0R}(H^{2}_{R+}(M)) is Artinian if and only if H^{i+2}_{\mathfrakm0R}(H^{1}_{R+}(M)) is Artinian, where cd(R_{+},M) is the cohomological dimension of M with respect to R_{+}. This improves some results of R. Sazeedeh.
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