One-sided EP elements in rings with involution

Authors

  • Cang Wu College of Science, Nanjing Forestry University, 210037 Nanjing, People's Republic of China and School of Mathematics, Southeast University, 210096 Nanjing, People's Republic of China https://orcid.org/0000-0002-5487-6361
  • Jianlong Chen School of Mathematics, Southeast University, 210096 Nanjing, People's Republic of China https://orcid.org/0000-0002-6798-488X
  • Yu Chen School of Electronic Science and Engineering, Hunan University of Information Technology, Changsha 410151, People's Republic of China

DOI:

https://doi.org/10.33044/revuma.3572

Abstract

This paper investigates the one-sided EP property of elements in rings with involution. Let $R$ be a ring with involution $\ast$. Then $a \in R$ is said to be left (resp. right) EP if $a$ is Moore–Penrose invertible and $aR \subseteq a^{\ast}R$ (resp. $a^{\ast}R \subseteq aR$). Many properties of EP elements are extended to one-sided versions. Some new characterizations of EP elements are presented in relation to the absorption law for Moore–Penrose inverses.

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Published

2024-10-07

Issue

Vol. 67 No. 2 (2024)

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Article

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Copyright (c) 2024 Cang Wu, Jianlong Chen, Yu Chen

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