Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON NI AND QUASI-NI RINGS

  • Kim, Dong Hwa (Department of Mathematics Education Pusan National University) ;
  • Lee, Seung Ick (Department of Mathematics Pusan National University) ;
  • Lee, Yang (Department of Mathematics Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics Pusan National University)
  • Received : 2016.03.23
  • Accepted : 2016.07.11
  • Published : 2016.09.30
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Abstract

Let R be a ring. It is well-known that R is NI if and only if ${\sum}^n_{i=0}Ra_i$ is a nil ideal of R whenever a polynomial ${\sum}^n_{i=0}a_ix^i$ is nilpotent, where x is an indeterminate over R. We consider a condition which is similar to the preceding one: ${\sum}^n_{i=0}Ra_iR$ contains a nonzero nil ideal of R whenever ${\sum}^n_{i=0}a_ix^i$ over R is nilpotent. A ring will be said to be quasi-NI if it satises this condition. The structure of quasi-NI rings is observed, and various examples are given to situations which raised naturally in the process.

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References

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