Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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IFP RINGS AND NEAR-IFP RINGS

  • Ham, Kyung-Yuen (Department of Mathematics Korea Science Academy) ;
  • Jeon, Young-Cheol (Department of Mathematics Korea Science Academy) ;
  • Kang, Jin-Woo (Department of Mathematics Korea Science Academy) ;
  • Kim, Nam-Kyun (College of Liberal Arts Hanbat National University) ;
  • Lee, Won-Jae (Department of Mathematics Korea Science Academy) ;
  • Lee, Yang (Department of Mathematics Education Busan National University) ;
  • Ryu, Sung-Ju (Department of Mathematics Busan National University) ;
  • Yang, Hae-Hun (Department of Mathematics Korea Science Academy)
  • Published : 2008.05.31
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Abstract

A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for $a,b{\in}R$. Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that ${\sum}^n_{i=0}$ $E_{ai}E$ is a nonzero nilpotent ideal of E whenever R is an IFP ring and $0{\neq}f{\in}F$ is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and $a_i^{'s}$ are the coefficients of f. we shall use the term near IFP to denote such a ring as having place near at the IFPness. In the present note the structures of IFP rings and near-IFP rings are observed, extending the classes of them. IFP rings are NI (i.e., nilpotent elements form an ideal). It is shown that the near-IFPness and the NIness are distinct each other, and the relations among them and related conditions are examined.

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References

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