Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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INSERTION-OF-FACTORS-PROPERTY ON NILPOTENT ELEMENTS

  • Baek, Jin-Eon (Department of Mathematics Korea Science Academy of KAIST) ;
  • Chin, Woo-Young (Department of Mathematics Korea Science Academy of KAIST) ;
  • Choi, Ji-Woong (Department of Mathematics Korea Science Academy of KAIST) ;
  • Eom, Tae-Hyun (Department of Mathematics Korea Science Academy of KAIST) ;
  • Jeon, Young-Cheol (Department of Mathematics Korea Science Academy of KAIST) ;
  • Lee, Yang (Department of Mathematics Pusan National University)
  • Received : 2010.11.10
  • Published : 2012.03.31
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Abstract

We generalize the insertion-of-factors-property by setting nilpotent products of elements. In the process we introduce the concept of a nil-IFP ring that is also a generalization of an NI ring. It is shown that if K$\ddot{o}$the's conjecture holds, then every nil-IFP ring is NI. The class of minimal noncommutative nil-IFP rings is completely determined, up to isomorphism, where the minimal means having smallest cardinality.

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