摘要
定义了 Artin 分次环的弱幂零分次根,并证明了一个 Artin 分次环 A 是半单的(即 A 的根为零)当且仅当 A 是有限个单 Artin 分次环的直和.这样连同已知的关于单 Artin 分次环的结构定理,便有了关于 Artin 分次环的所有基本结构定理.
The author gives a definition of weakly nilpotent graded radical for artinian graded rings and prove that an artinian graded ring A is semi- simple(i.e.the radical of A is zero)if and if A is a direct sum of finite number of simple artinian graded rings.So together with a well-known re- sult on structure of simple artinian graded rings the author obtains all basic structure theorems for artinian graded rings.
出处
《北京师范大学学报（自然科学版）》
CAS
CSCD
1989年第3期22-25,共4页
Journal of Beijing Normal University(Natural Science)
基金
国家自然科学基金
关键词
Artin分次环
半单
弱幂零分次根
artinian graded rings, weakly nilpotent graded radical, semi-simple artinian graded rings
