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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (2): 84-90.doi: 10.6040/j.issn.1671-9352.0.2018.711

• • 上一篇    

JGR-clean环

徐莹莹,殷晓斌*   

  1. 安徽师范大学数学与统计学院, 安徽 芜湖 241003
  • 发布日期:2020-02-14
  • 作者简介:徐莹莹(1993— ),女,硕士研究生,研究方向为环论. E-mail:352884332@qq.com*通信作者简介:殷晓斌(1972— ),男,博士,教授,研究方向为环论. E-mail:xbyinzh@ahnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11401009);安徽省高校自然科学重点基金资助项目(KJ2019A0488)

On JGR-clean rings

XU Ying-ying, YIN Xiao-bin*   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003, Anhui, China
  • Published:2020-02-14

摘要: 引入了(强)JGR-clean环的概念。说明了JGR-clean环是 J-clean环的真推广,研究了(强)JGR-clean环的一些基本性质以及扩张,同时讨论了(强)JGR-clean环与一些特殊环之间的关系。

关键词: J-clean环, π-正则环, π-正则环, JGR-clean环, 强JGR-clean环

Abstract: The concepts of(strongly)JGR-clean rings are introduced. It is proved that JGR-clean rings are the real generalization of J-clean rings. Basic properties and extension properties of such rings are investigated. Moreover, the relationships between(strongly)JGR-clean rings and some special rings are discussed.

Key words: J-clean rings, π-regular rings, strongly π-regular rings, JGR-clean rings, strongly JGR-clean rings

中图分类号: 

  • O153.3
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