Title & Authors
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 $\small{\in}$ 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
Language
English
Cited by
1.
On Commutativity of Semiprime Right Goldie C<i><sub>k</sub></i>-Rings, Advances in Pure Mathematics, 2012, 02, 04, 217
2.
ON WEAK ZIP SKEW POLYNOMIAL RINGS, Asian-European Journal of Mathematics, 2012, 05, 03, 1250039
3.
Mal’cev-Neumann series over rings satisfy the weak Beachy–Blair condition, Rendiconti del Circolo Matematico di Palermo (1952 -), 2016
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