IFP RINGS AND NEAR-IFP RINGS

Title & Authors
IFP RINGS AND NEAR-IFP RINGS
Ham, Kyung-Yuen; Jeon, Young-Cheol; Kang, Jin-Woo; Kim, Nam-Kyun; Lee, Won-Jae; Lee, Yang; Ryu, Sung-Ju; Yang, Hae-Hun;

Abstract
A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for $\small{a,b{\in}R}$. Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that $\small{{\sum}^n_{i=0}}$ $\small{E_{ai}E}$ is a nonzero nilpotent ideal of E whenever R is an IFP ring and $\small{0{\neq}f{\in}F}$ is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and $\small{a_i^{$ 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.
Keywords
IFP ring;near-IFP ring;reduced ring;NI ring;polynomial ring;matrix ring;nilpotent ideal;
Language
English
Cited by
1.
ON CONDITIONS PROVIDED BY NILRADICALS,Kim, Hong-Kee;Kim, Nam-Kyun;Jeong, Mun-Seob;Lee, Yang;Ryu, Sung-Ju;Yeo, Dong-Eun;

대한수학회지, 2009. vol.46. 5, pp.1027-1040
1.
On Commutativity of Semiprime Right Goldie C<i><sub>k</sub></i>-Rings, Advances in Pure Mathematics, 2012, 02, 04, 217
2.
ON CONDITIONS PROVIDED BY NILRADICALS, Journal of the Korean Mathematical Society, 2009, 46, 5, 1027
3.
ON SEMI-IFP RINGS, Korean Journal of Mathematics, 2015, 23, 1, 37
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