Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WHEN NILPOTENTS ARE CONTAINED IN JACOBSON RADICALS

  • Lee, Chang Ik (Department of Mathematics Pusan National University) ;
  • Park, Soo Yong (Department of Mathematics Pusan National University)
  • Received : 2017.10.01
  • Accepted : 2017.11.29
  • Published : 2018.09.01
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Abstract

We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be NJ if it satisfies such property. We prove the following: (i) $K{\ddot{o}}the^{\prime}s$ conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If R is an NJ ring, then R is exchange if and only if it is clean; and (iii) A ring R is NJ if and only if so is every (one-sided) corner ring of R.

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References

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