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Artinianess of graded local cohomology modules

Authors:	Reza Sazeedeh

Affiliation:	Department of Mathematics, Urmia University, Urmia, Iran --and-- Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran

Abstract:	Let $R=bigoplus_{n in mathbb{N}} R_n$ be a Noetherian homogeneous ring with local base ring $(R_0, mathfrak{m}_0)$ and let be a finitely generated graded -module. Let be the largest integer such that $H_{R_+}^a(M)$ is not Artinian. We will prove that $H_{R_+}^i(M)/mathfrak{m}_0H_{R_+}^i(M)$ are Artinian for all and there exists a polynomial of degree less than such that ${rm length}_{R_0}(H_{R_+}^a(M)_n /mathfrak{m}_0H_{R_+}^a(M)_n) =widetilde{P}(n)$ for all . Let be the first integer such that the local cohomology module $H_{R_+}^s(M)$ is not ${R_+}-$ cofinite. We will show that for all the graded module $Gamma_{mathfrak{m}_0}(H_{R_+}^i(M))$ is Artinian.

Keywords:	Graded local cohomology Artinian module polynomial

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