Artinian and Non-Artinian Local Cohomology Modules

Canadian mathematical bulletin

Mohammad T. Dibaei¹  Alireza Vahidi¹ 

[1] Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, Tehran, Iran

关键词: local cohomology modules;    cohomological dimensions;    Bass numbers;   

DOI  :  10.4153/CMB-2011-042-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $M$ be a finite module over a commutative noetherian ring $R$. For ideals $mathfrak{a}$ and $mathfrak{b}$ of $R$, the relations between cohomological dimensions of $M$ with respect to $mathfrak{a}, mathfrak{b}$, $mathfrak{a}capmathfrak{b}$ and $mathfrak{a}+ mathfrak{b}$ are studied. When $R$ is local, it is shown that $M$ is generalized Cohen-Macaulay if there exists an ideal $mathfrak{a}$ such that all local cohomology modules of $M$ with respect to $mathfrak{a}$ have finite lengths. Also, when $r$ is an integer such that $0leq r< dim_R(M)$, any maximal element $mathfrak{q}$ of the non-empty set of ideals ${mathfrak{a} : extrm{H}_mathfrak{a}^i(M)$ is not artinian for some $ i, igeq r }$ is a prime ideal, and all Bass numbers of $extrm{H}_mathfrak{q}^i(M)$ are finite for all $igeq r$.

【 授权许可】

Unknown