East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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JACOBSON RADICAL AND NILPOTENT ELEMENTS

  • Huh, Chan (Department of Mathematics Pusan National University) ;
  • Cheon, Jeoung Soo (Department of Mathematics Pusan National University) ;
  • Nam, Sun Hye (Department of Mathematics Pusan National University)
  • Received : 2017.11.21
  • Accepted : 2018.01.24
  • Published : 2018.01.31
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Abstract

In this article we consider rings whose Jacobson radical contains all the nilpotent elements, and call such a ring an NJ-ring. The class of NJ-rings contains NI-rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

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References

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