On w-Linked Overrings  

作　　者：Lin XIE Fang Gui WANG Yan TIAN 

机构地区：[1]Department of Mathematics,Sichuan Normal University, Sichuan 610068, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第2期337-346,共10页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10671137);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060636001)

摘　　要：Let R ■ T be an extension of commutative rings.T is called w-linked over R if T as an R-module is a w-module.In the case of R ■ T ■ Q 0 （R）,T is called a w-linked overring of R.As a generalization of Wang-McCsland-Park-Chang Theorem,we show that if R is a reduced ring,then R is a w-Noetherian ring with w-dim（R） 1 if and only if each w-linked overring T of R is a w-Noetherian ring with w-dim（T ） 1.In particular,R is a w-Noetherian ring with w-dim（R） = 0 if and only if R is an Artinian ring.Let R ■ T be an extension of commutative rings.T is called w-linked over R if T as an R-module is a w-module.In the case of R ■ T ■ Q 0 （R）,T is called a w-linked overring of R.As a generalization of Wang-McCsland-Park-Chang Theorem,we show that if R is a reduced ring,then R is a w-Noetherian ring with w-dim（R） 1 if and only if each w-linked overring T of R is a w-Noetherian ring with w-dim（T ） 1.In particular,R is a w-Noetherian ring with w-dim（R） = 0 if and only if R is an Artinian ring.

关 键 词：GV -ideal w-module w-linked w-Noetherian ring 

分 类 号：O153.3[理学—数学]