On Medium *-Clean Rings

  • Huanyin ChenEmail author
  • Marjan Sheibani Abdolyousefi
  • Handan Kose


A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of an element in its Jacobson radical and a projection that commute. We prove that a ring R is medium *-clean if and only if R is strongly *-clean and R / J(R) is a Boolean ring, \({\mathbb {Z}}_3\) or the product of such rings, if and only if R weakly J-*-clean and \(a^2\in R\) is uniquely *-clean for all \(a\in R\), if and only if every idempotent lifts modulo J(R), R is abelian and R / J(R) weakly *-Boolean. A subclass of medium *-clean rings with many nilpotents is thereby characterized.


Projection Jacobson radical homomorphic image *-clean ring 

Mathematics Subject Classification

Primary 16W10 Secondary 16E50 



The authors would like to thank the referee for his/her careful reading and valuable remarks that improved the presentation of our work. H. Chen was supported by the Natural Science Foundation of Zhejiang Province, China (no. LY17A010018).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Huanyin Chen
    • 1
    Email author
  • Marjan Sheibani Abdolyousefi
    • 2
  • Handan Kose
    • 3
  1. 1.Department of MathematicsHangzhou Normal UniversityHangzhouChina
  2. 2.Women’s University of Semnan (Farzanegan)SemnanIran
  3. 3.Department of MathematicsAhi Evran UniversityKirsehirTurkey

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