On Flat and Gorenstein Flat Dimensions of Local Cohomology Modules

Canadian mathematical bulletin

Majid Rahro Zargar²  Hossein Zakeri¹ 

[1] Faculty of mathematical sciences and computer, Kharazmi University, 599 Taleghani Avenue, Tehran 15618, Iran;Department of Advanced Technologies, University of Mohaghegh ardabili, Namin, Ardabil, Iran

关键词: flat dimension;    Gorenstein injective dimension;    Gorenstein flat dimension;    local cohomology;    relative Cohen-Macaulay module;    semidualizing module;   

DOI  :  10.4153/CMB-2015-080-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $mathfrak{a}$ be an ideal of a Noetherian local ring $R$ and let $C$ be a semidualizing $R$-module. For an $R$-module $X$, we denote any of the quantities $mathfrak{d}_R X$,$operatorname{mathsf{Gfd}}_R X$ and $operatorname{mathsf{G_C-fd}}_RX$ by $operatorname{mathsf{T}}(X)$. Let $M$ be an $R$-module such that$operatorname{H}_{mathfrak{a}}^i(M)=0$ for all $ieq n$. It is proved that if $operatorname{mathsf{T}}(X)lt infty$, then $operatorname{mathsf{T}}(operatorname{H}_{mathfrak{a}}^n(M))leqoperatorname{mathsf{T}}(M)+n$ and the equality holds whenever $M$ is finitely generated. With the aid of these results, among other things, we characterize Cohen-Macaulay modules, dualizingmodules and Gorenstein rings.

【 授权许可】

Unknown