群环上的强J-clean矩阵

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1587-1591.

群环上的强J-clean矩阵

陈焕艮

杭州师范大学理学院 310036

收稿日期:2013-07-14 修回日期:2014-04-16 出版日期:2014-12-25 发布日期:2014-12-25
基金资助:
浙江省自然科学基金(LY13A010019)资助

Strongly J-clean Matrices over Group Rings

CHEN Huan-Yin

Department of Mathematics, Hangzhou Normal University, Hangzhou 310036

Received:2013-07-14 Revised:2014-04-16 Online:2014-12-25 Published:2014-12-25
Supported by:
浙江省自然科学基金(LY13A010019)资助

摘要/Abstract

摘要：

设R 是一个环, J(R) 表示 $R$ 的Jacbson 根. R 的一个元素称为强J-clean 的, 如果能够表示成一个幂等元和一个J(R) 中元素的和且这两个元素可交换. 对于一个可交换局部环R 满足2∈J(R), 得到一个在RG 上2×2 矩阵是强J-clean 的充要条件, 其中G= {1, g} 是一个群. 同时给出了强clean性的上应用.

关键词: 强J-clean元, 2×2矩阵, 交换局部环

Abstract:

Let R be a ring, and let J(R) be the Jacobson radical of R. An element of a ring R is called strongly J-clean provided
that it can be written as the sum of an idempotent and an element in J(R) that commute. For a commutative local ring R with 2∈J(R), we get a necessary and sufficient condition under which a 2×2 matrix over RG is strongly J-clean where
G={ 1, g} is a group. An application to strong cleanness is also obtained

Key words: Strongly J-clean element, 2×2 Matrix, Commutative local ring

中图分类号:

16E50

陈焕艮. 群环上的强J-clean矩阵[J]. 数学物理学报, 2014, 34(6): 1587-1591.

CHEN Huan-Yin. Strongly J-clean Matrices over Group Rings[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1587-1591.