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DOI QR Code

NIL-CLEAN RINGS OF NILPOTENCY INDEX AT MOST TWO WITH APPLICATION TO INVOLUTION-CLEAN RINGS

  • Li, Yu (School of Mathematics and Statistics Southwest University) ;
  • Quan, Xiaoshan (School of Mathematics and Statistics Guangxi Teachers Education University) ;
  • Xia, Guoli (Department of Mathematics and Statistics Memorial University of Newfoundland)
  • Received : 2017.07.25
  • Accepted : 2017.09.06
  • Published : 2018.07.31

Abstract

A ring is nil-clean if every element is a sum of a nilpotent and an idempotent, and a ring is involution-clean if every element is a sum of an involution and an idempotent. In this paper, a description of nil-clean rings of nilpotency index at most 2 is obtained, and is applied to improve a known result on involution-clean rings.

Keywords

idempotent;nilpotent;involution;nil-clean ring of nilpotency index at most 2;involution-clean ring

Acknowledgement

Supported by : National Natural Science Foundation of China, Guangxi Natural Science Foundation, Guangxi Education Department

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