强g(x)-J-Clean环

doi:10.6040/j.issn.1671-9352.0.2016.269

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (2): 24-29.doi: 10.6040/j.issn.1671-9352.0.2016.269

强g(x)-J-Clean环

高汉鹏,殷晓斌^*

安徽师范大学数学计算机科学学院, 安徽芜湖 241003

收稿日期:2016-06-14 出版日期:2017-02-20 发布日期:2017-01-18
通讯作者: 殷晓斌(1972— ), 男, 博士, 教授, 研究方向为环论.E-mail:xbyinzh@mail.ahnu.edu.cn E-mail:hpgao07@163.com
作者简介:高汉鹏(1991— ), 男, 硕士研究生,研究方向为环论.E-mail:hpgao07@163.com
基金资助:
国家自然科学基金资助项目(11401009);安徽省自然科学基金资助项目(1408085QA01);2015年安徽师范大学研究生科研创新与实践资助项目(2015cxsj116)

On strongly g(x)-J-clean rings

GAO Han-peng, YIN Xiao-bin^*

College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China

Received:2016-06-14 Online:2017-02-20 Published:2017-01-18

摘要/Abstract

摘要： 介绍了强g(x)-J-clean环的概念。说明了强J-clean环是强x(x-1)-J-clean环。给出了强g(x)-J-clean环以及强J-clean 环的一些等价刻画。同时证明了强(xⁿ-x)-J-clean环是直有限的且有稳定秩1(n≥2)。

关键词: J-clean环, g(x)-clean环, clean环, 强g(x)-J-clean环

Abstract: The concept of strongly g(x)-J-clean rings is introduced. It is proved strongly J-clean rings are strongly x(x-1)-J-clean. Moreover, equivalent characters for strongly g(x)-J-clean rings and J-clean rings are given. It is proved that strongly (xⁿ-x)-J-clean rings are directly finite and have stable range one (n≥2).

Key words: clean rings, strongly J-clean rings, strongly g(x)-J-clean rings, g(x)-clean rings

中图分类号:

O153.3

高汉鹏,殷晓斌. 强g(x)-J-Clean环[J]. 山东大学学报（理学版）, 2017, 52(2): 24-29.

GAO Han-peng, YIN Xiao-bin. On strongly g(x)-J-clean rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 24-29.

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