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EP Elements in Rings with Involution

  • Sanzhang XuEmail author
  • Jianlong Chen
  • Julio Benítez
Article
  • 13 Downloads

Abstract

Let R be a unital ring with involution. We first show that the EP elements in R can be characterized by three equations. Namely, let \(a\in R\), then a is EP if and only if there exists \(x\in R\) such that \((xa)^{*}=xa\), \(xa^{2}=a\) and \(ax^{2}=x.\) Any EP element in R is core invertible and Moore–Penrose invertible. We give more equivalent conditions for a core (Moore–Penrose) invertible element to be an EP element. Finally, any EP element is characterized in terms of the n-EP property, which is a generalization of the bi-EP property.

Keywords

Core inverse EP bi-EP n-EP 

Mathematics Subject Classification

15A09 16W10 16U80 

Notes

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 11771076). The first author is grateful to China Scholarship Council for giving him a purse for his further study in Universitat Politècnica de València, Spain.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsHuaiyin Institute of TechnologyHuaianChina
  2. 2.School of MathematicsSoutheast UniversityNanjingChina
  3. 3.Universitat Politècnica de ValènciaInstituto de Matemática MultidisciplinarValenciaSpain

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