Artinianness of Certain Graded Local Cohomology Modules

Canadian mathematical bulletin

Amir Mafi²  Hero Saremi¹ 

[1] Department of Mathematics, Islamic Azad University, Sanandaj Branch, Sanandaj, Iran;Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran

关键词: graded local cohomology;    Artinian modules;   

DOI  :  10.4153/CMB-2011-044-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We show that if$R=igoplus_{ninmathbb{N}_0}R_n$ is a Noetherian homogeneous ringwith local base ring $(R_0,mathfrak{m}_0)$, irrelevant ideal $R_+$, and$M$ a finitely generated graded $R$-module, then$H_{mathfrak{m}_0R}^j(H_{R_+}^t(M))$ is Artinian for $j=0,1$ where$t=inf{iin{mathbb{N}_0}: H_{R_+}^i(M)$ is not finitelygenerated $}$. Also, we prove that if $operatorname{cd}(R_+,M)=2$, then foreach $iinmathbb{N}_0$, $H_{mathfrak{m}_0R}^i(H_{R_+}^2(M))$ isArtinian if and only if $H_{mathfrak{m}_0R}^{i+2}(H_{R_+}^1(M))$ isArtinian, where $operatorname{cd}(R_+,M)$ is the cohomological dimension of $M$with respect to $R_+$. This improves some results of R. Sazeedeh.

【 授权许可】

Unknown