强π-正则斜群环的一些性质  

Some Properties of Strongly π-Regular Skew Group Rings

作　　者：高艳艳 GAO Yanyan(Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, Jiangsu)

机构地区：[1]南京工程学院数理部,江苏南京211167

出　　处：《四川师范大学学报（自然科学版）》2017年第5期651-654,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：江苏省自然科学基金青年基金(BK20160771)

摘　　要：设R是有单位元的结合环.设x∈R,若存在y∈R和正整数n,使得x^n=yx^(n+2)(x^n=x^(n+1)y),则称x是左(右)π-正则元.如果x既是左π-正则元又是右π-正则元,则称x是强π-正则元.若环R中的每一个元素都是强π-正则元,则称R是强π-正则环.给出了R*_θG是强π-正则的充分或必要条件,其中θ是群G到由R的自同构所构成的群Aut(R)的群同态.Let R be an associative ring with identity. An element x ∈ R is said to be left （right） π-regular if there exists y ∈ R and a positive integer n such that xn =yxn＋2（xn =xn＋1y）. Ifx is both left and right π-regu/ar, then it is said to be strongly or-regular. A ring R is said to be a strongly or-regular ring if all elements are strongly π-regular. In this paper, we determine some conditions which are either necessary or sufficient for a skew group ring R ＊ 0G to be strongly or-regular, where θ is a group homomorphism from a group G to Aut（R）, the group of automorphisms of R.

关 键 词：强π-正则 斜群环 G-素理想 

分 类 号：O153.3[理学—数学]