[1]沈 磊,王芳贵*,王 茜.g(x)-J-clean环[J].四川师范大学学报(自然科学版),2018,(04):483-488.[doi:10.3969/j.issn.1001-8395.2018.04.009]
 SHEN Lei,WANG Fanggui,WANG Xi.g(x)-J-clean Rings[J].Journal of SichuanNormal University,2018,(04):483-488.[doi:10.3969/j.issn.1001-8395.2018.04.009]
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年04期
页码:
483-488
栏目:
基础理论
出版日期:
2018-04-15

文章信息/Info

Title:
g(x)-J-clean Rings
文章编号:
1001-8395(2018)04-0483-06
作者:
沈 磊 王芳贵* 王 茜
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
SHEN Lei WANG Fanggui WANG Xi
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
clean环 g(x)-J-clean环 g(x)-clean环 J-clean环 弱clean环 有限域
Keywords:
clean ring g(x)-J-clean ring g(x)-clean ring J-clean ring weakly clean ring finite field
分类号:
O153
DOI:
10.3969/j.issn.1001-8395.2018.04.009
文献标志码:
A
摘要:
设R是环,J(R)和C(R)分别表示R的Jacobson根与中心,g(x)∈C(R)[x]为一给定多项式.称R为g(x)-J-clean环,如果任何r∈R可表为r=s+j,其中j∈J(R)且g(s)=0.给出g(x)-J-clean环的基本性质,并给出一些J-clean环的等价刻画,考察(x3-x)-clean环与弱clean环的关系,也证明(xn-1)-J*-clean环就是有限域.
Abstract:
Let R be a ring, J(R) and C(R) denote the Jacobson radical and the center respectively, and g(x)∈C(R)[x] is a given polynomial.R is called g(x)-J-clean ring, if any r∈R can be written as r=s+j, where j∈J(R) and g(s)=0.We obtained some basic properties of g(x)-J-clean rings and some equivalent conditions of J-clean rings.We studied the relations between (x3-x)-clean rings and weakly clean rings, and proved that an (xn-1)-J*-clean ring is a finite field.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-03-03 接受日期:2017-05-04
基金项目:国家自然科学基金(11171240)
*通信作者简介:王芳贵(1955—),男,教授,主要从事交换代数、同调代数的研究,E-mail:wangfg2004@163.com
更新日期/Last Update: 2018-04-15