JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 13-17.doi: 10.6040/j.issn.1671-9352.0.2022.345

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Some equivalent characterizations on EP elements

Mengge GUAN(),Hainan ZHOU,Junchao WEI*()   

  1. College of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Received:2022-06-23 Online:2023-08-20 Published:2023-07-28
  • Contact: Junchao WEI E-mail:2530374647@qq.com;jcwei@yzu.edu.cn

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Abstract:

By studying the properties of EP elements and their association with idempotents and Jacobson radicals, some equivalent characterizations of EP elements are presented. A new structure is introduced to facilitate the equivalent characterizations of EP elements through Moore-Penrose(MP) inverses and the relationship between group inverses. Finally, by constructing some equations on the ring, the equivalent characterizations of EP elements are established by finding solutions on specific sets.

Key words: EP element, Moore-Penrose(MP) inverse, group inverse, involution ring

CLC Number: 

  • O153.3
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