ON CONDITIONS PROVIDED BY NILRADICALS

- Journal title : Journal of the Korean Mathematical Society
- Volume 46, Issue 5, 2009, pp.1027-1040
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2009.46.5.1027

Title & Authors

ON CONDITIONS PROVIDED BY NILRADICALS

Kim, Hong-Kee; Kim, Nam-Kyun; Jeong, Mun-Seob; Lee, Yang; Ryu, Sung-Ju; Yeo, Dong-Eun;

Kim, Hong-Kee; Kim, Nam-Kyun; Jeong, Mun-Seob; Lee, Yang; Ryu, Sung-Ju; Yeo, Dong-Eun;

Abstract

A ring R is called IFP, due to Bell, if ab = 0 implies aRb = 0 for a, b 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;

Language

English

Cited by

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