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- 저자 : Ham Kyung-Yuen (검색결과 1 건)
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Ham, Kyung-Yuen,Jeon, Young-Cheol,Kang, Jin-Woo,Kim, Nam-Kyun,Lee, Won-Jae,Lee, Yang,Ryu, Sung-Ju,Yang, Hae-Hun Korean Mathematical Society 2008 대한수학회지 Vol.45 No.3
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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