Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS

  • Chun, Young (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY) ;
  • Jeon, Young-Cheol (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY) ;
  • Kang, Sung-Kyung (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY) ;
  • Lee, Key-Nyoung (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY) ;
  • Lee, Yang (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
  • Received : 2009.05.18
  • Published : 2011.01.31
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Abstract

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

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References

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