吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (3): 577-582.

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广义n-强Drazin逆的注记

李明珠, 宋贤梅   

  1. 安徽师范大学 数学与统计学院, 安徽 芜湖 241002
  • 收稿日期:2021-08-08 出版日期:2022-05-26 发布日期:2022-05-26
  • 通讯作者: 宋贤梅 E-mail:xianmeisongahnu@163.com

Notes on Generalized n-Strong Drazin Inverse

LI Mingzhu, SONG Xianmei   

  1. College of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui Province, China
  • Received:2021-08-08 Online:2022-05-26 Published:2022-05-26

摘要: 首先, 在条件acd=dbd, bdb=bac下给出广义n-强Drazin可逆元的Cline公式及Jacobson引理; 其次, 给出广义n-强Drazin可逆的幂等元相等的等价刻画; 最后, 在条件acd=dbd, dba=aca下讨论广义n-强Drazin可逆元相似的等价刻画以及多元素相似性问题.

关键词: 广义n-强Drazin逆, 相似, 单位正则环

Abstract: Firstly, the Cline’s formula and Jacobson’s lemma for generalized n-strong Drazin inverse were given under the conditions of acd=dbd, bdb=bac. Secondly, the equivalent characterizations of generalized n-strong Drazin inverse idempotent elements equality were given. Finally, the equivalent characterizations of generalized n-strong Drazin invertible element similarity and the problem of multi-element similarity under the condition of acd=dbd, dba=aca were discussed.

Key words: generalized n-strong Drazin inverse, similar, unit regular ring

中图分类号: 

  • O153.3