UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES

被引：0
|
作者：
Zhao, Renyu [1 ]
机构：
[1] NW Normal Univ, Coll Econ & Management, Lanzhou 730070, Peoples R China
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 05期
基金：
中国国家自然科学基金;
关键词：
skew generalized power series ring; generalized inverse polynomial module; uniform dimension; couniform dimension; GOLDIE-DIMENSION; RINGS;
D O I：
10.4134/BKMS.2012.49.5.1067
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M be a right R-module, (S, <=) a strictly totally ordered monoid which is also artinian and omega : S -> Aut(R) a monoid homomorphism, and let [M-S,M-<=]([[RS,<=,omega]]) denote the generalized inverse polynomial module over the skew generalized power series ring [[R-S,R-<=, omega]]. In this paper, we prove that [M-S,M-<=]([[RS,<=,omega]]) has the same uniform dimension as its coefficient module M-R, and that if, in addition, R is a right perfect ring and S is a chain monoid, then [M-S,M-<=]([[RS,<=,omega]]) has the same couniform dimension as its coefficient module M-R.
引用
收藏
页码：1067 / 1079
页数：13
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