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

作　　者：Le Thanh Nhan Tran Do Minh Chau 

机构地区：[1]Thai Nguyen College of Sciences, Thai Nguyen, Vietnam

出　　处：《Algebra Colloquium》2014年第4期663-670,共8页代数集刊（英文版）

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.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.

关 键 词：Artinian modules CO-LOCALIZATION going up formal fibers 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论] O153.3[自动化与计算机技术—计算机科学与技术]