Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON S-EXCHANGE RINGS

  • Liu, Dajun (School of Mathematics and Physics Anhui Polytechnic University) ;
  • Wei, Jiaqun (Institute of Mathematics School of Mathematics Sciences Nanjing Normal University)
  • Received : 2019.07.01
  • Accepted : 2020.06.04
  • Published : 2020.07.31
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Abstract

We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.

Keywords

Acknowledgement

The authors are very grateful to Professor Jian Cui for the comments, corrections and suggestions. The authors would like to thank the referee for helpful valuable comments and suggestions on the last version of the paper.

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