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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (11): 70-78.doi: 10.6040/j.issn.1671-9352.0.2023.553

• • 上一篇    

拟J-*-clean环

李筱璇,殷晓斌*   

  1. 安徽师范大学数学与统计学院, 安徽 芜湖 241002
  • 发布日期:2025-11-11
  • 通讯作者: 殷晓斌(1972— ),男,教授,博士,研究方向为同调代数与环论. E-mail:xbyinzh@ahnu.edu.cn
  • 作者简介:李筱璇(1999— ),女,硕士研究生,研究方向为环论. E-mail:2194286835@qq.com
  • 基金资助:
    安徽省自然科学基金资助项目(2008085MA06);安徽省教育厅重点资助项目(gxyqZD2019009)

Quasi J-*-clean rings

LI Xiaoxuan, YIN Xiaobin*   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China
  • Published:2025-11-11

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摘要： 若该环中所有元素都表示为一个拟投射元与一个Jacobson根中元素之和(且它们可以交换),称该环是(强)拟J-*-clean环。本文研究了拟J-*-clean环的基本性质以及其与其他*-环的关系,证明R是强拟J-*-clean环当且仅当R是强*-clean环且R/J(R)是强拟J-*-clean环,当且仅当R/J(R)是强拟J-*-clean环,R中投射元是中心的且投射元模J(R)可提升。

关键词: clean环, *-环, 拟J-clean环, 拟J-*-clean环, 强拟J-*-clean环

Abstract: A ring is called(strongly)quasi J-*-clean ring if each of its elements is a sum of a quasi-projection and an element of the Jacobson radical(that commute). The basic properties of this ring and some relations with other rings are studied. It is proved that R is a strongly quasi J-*-clean ring if and only if R is a strongly *-clean ring and R/J(R) is a strongly quasi J-*-clean ring if and only if R/J(R) is a strongly quasi J-*-clean ring, every projection of R is central and every projection of R/J(R) is lifted to a projection of R.

Key words: clean ring, *-ring, quasi J-clean ring, quasi J-*-clean ring, strongly quasi J-*-clean ring

中图分类号: 

  • O153.3
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