Vanishing of the top local cohomology modules over Noetherian rings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Vanishing of the top local cohomology modules over Noetherian rings

Authors:

Kamran Divaani-Aazar

Institution:

(1) Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran

Abstract:

Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let $\mathfrak{a}$ be an ideal of R and $\mathfrak{M}$ denote the intersection of all prime ideals $\mathfrak{p} \in Supp_R H_\mathfrak{a}^d (M)$ . It is shown that

$H_\mathfrak{a}^d (M) \simeq H_\mathfrak{M}^d (M)/\sum\limits_{n \in \mathbb{N}} {\langle \mathfrak{M}\rangle } (0:_{H_\mathfrak{M}^d (M)} \mathfrak{a}^n ),$

where for an Artinian R-module A we put $\langle \mathfrak{M}\rangle A = \cap _{n \in \mathbb{N}} \mathfrak{M}^n$ A. As a consequence, it is proved that for all ideals $\mathfrak{a}$ of R, there are only finitely many non-isomorphic top local cohomology modules $H_\mathfrak{a}^d (M)$ having the same support. In addition, we establish an analogue of the Lichtenbaum-Hartshorne vanishing theorem over rings that need not be local.

Keywords:

Artinian modules attached prime ideals cohomological dimension formally isolated local cohomology secondary representations

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏