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http://dx.doi.org/10.4134/JKMS.2009.46.5.1027

ON CONDITIONS PROVIDED BY NILRADICALS  

Kim, Hong-Kee (DEPARTMENT OF MATHEMATICS GYEONGSANG NATIONAL UNIVERSITY)
Kim, Nam-Kyun (DIVISION OF GENERAL EDUCATION HANBAT NATIONAL UNIVERSITY)
Jeong, Mun-Seob (DEPARTMENT OF MATHEMATICS BUSAN NATIONAL UNIVERSITY)
Lee, Yang (DEPARTMENT OF MATHEMATICS EDUCATION BUSAN NATIONAL UNIVERSITY)
Ryu, Sung-Ju (DEPARTMENT OF MATHEMATICS BUSAN NATIONAL UNIVERSITY)
Yeo, Dong-Eun (DEPARTMENT OF MATHEMATICS BUSAN NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.5, 2009 , pp. 1027-1040 More about this Journal
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 is not preserved by polynomial ring extensions. In this note we concentrate on a generalized condition of the IFPness that can be lifted up to polynomial rings, introducing the concept of quasi-IFP rings. The structure of quasi-IFP rings will be studied, characterizing quasi-IFP rings via minimal strongly prime ideals. The connections between quasi-IFP rings and related concepts are also observed in various situations, constructing necessary examples in the process. The structure of minimal noncommutative (quasi-)IFP rings is also observed.
Keywords
IFP ring; quasi-IFP ring; Wedderburn radical; nilradical; polynomial ring;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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