J-周期环及其扩张  

J-periodic Ring and Extensions

作　　者：马彪[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2013年第4期354-358,384,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：杭州师范大学创新种子基金项目

摘　　要：定义了J-周期环,推广了周期环.首先,讨论J-周期环的一些基本性质,如J-周期环的商环、子环以及J-周期环与周期环的关系.然后,给出J-周期环的一些扩张,并证明环的J-周期性与其上的幂级数环、广义矩阵环、上三角矩阵环的J-周期性是等价的.This paper defined J-periodic ring which generalized the concept of periodic ring. Firstly, some elementary properties of J-periodic rings were studied , such as the quotient rings and subrings of J-periodic rings as well as the relationship between J-periodic rings and periodic rings. Then some extensions of J-periodic rings were provided, and the equivalence of the J-periodicity of a ring and the J-periodicity of the power series ring, generalized matrix ring and upper triangular matrix ring over it was proved.

关 键 词：周期环 J-周期环 JACOBSON根 广义矩阵环 扩张 

分 类 号：O153.3[理学—数学]