Noetherian Dimension and Co-localization of Artinian Modules over Local Rings

• 作者: Le Thanh Nhan Tran Do Minh Chau
• 来源期刊: 代数集刊:英文版
• 学科: 工学
• 关键词: 生成模块 局部环 尺寸 本地化 R-模 共定位 接触网 兼容
• 年，卷（期）: 2014,（4）
• 页码范围: 663-670
• 页数: 8页
• 分类号: TP311
• 语种: 中文

摘要

Let (R,m) be a Noetherian local ring. Denote by N-dimnA the Noetherian dimension of an Artinian R-module A. In this paper, we give some characterizations for the ring R to satisfy N-dimRA = dim(R/AnnRA) for certain Artinian R-modules A. Then the existence of a co-localization compatible with Artinian R-modules is studied and it is shown that if it is compatible with local cohomologies of finitely generated modules, then the base ring is universally catenary and all of its formal fibers are Cohen-Macaulay.