Artinianness of Certain Graded Local Cohomology Modules

Abstract

AbstractWe show that ifR= ⴲn∈ℕ0Rnis a Noetherian homogeneous ring with local base ring (R0, m0), irrelevant idealR+, andMa finitely generated gradedR-module, thenis Artinian forj= 0, 1 wheret= inf﹛i∈ ℕ0:is not finitely generated﹜. Also, we prove that if cd(R+,M) = 2, then for eachi∈ ℕ0,) is Artinian if and only ifis Artinian, where cd(R+,M) is the cohomological dimension ofMwith respect toR+. This improves some results of R. Sazeedeh.