JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (2): 24-29.doi: 10.6040/j.issn.1671-9352.0.2016.269

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On strongly g(x)-J-clean rings

GAO Han-peng, YIN Xiao-bin*   

  1. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2016-06-14 Online:2017-02-20 Published:2017-01-18

Abstract: The concept of strongly g(x)-J-clean rings is introduced. It is proved strongly J-clean rings are strongly x(x-1)-J-clean. Moreover, equivalent characters for strongly g(x)-J-clean rings and J-clean rings are given. It is proved that strongly (xn-x)-J-clean rings are directly finite and have stable range one (n≥2).

Key words: clean rings, strongly J-clean rings, strongly g(x)-J-clean rings, g(x)-clean rings

CLC Number: 

  • O153.3
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