Bull. Korean Math. Soc. 2012; 49(2): 381-394
Printed March 1, 2012
https://doi.org/10.4134/BKMS.2012.49.2.381
Copyright © The Korean Mathematical Society.
Jineon Baek, Wooyoung Chin, Jiwoong Choi, Taehyun Eom, Young Cheol Jeon, and Yang Lee
Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Pusan National University
We generalize the insertion-of-factors-property by setting nilpotent products of elements. In the process we introduce the concept of a $nil$-$IFP$ ring that is also a generalization of an NI ring. It is shown that if K\"othe's conjecture holds, then every nil-IFP ring is NI. The class of minimal noncommutative nil-IFP rings is completely determined, up to isomorphism, where the minimal means having smallest cardinality.
Keywords: nilpotent element, IFP ring, nil-IFP ring, NI ring, polynomial ring
MSC numbers: 16N40, 16U80, 16S36
2019; 56(4): 993-1006
2017; 54(2): 521-541
2023; 60(6): 1523-1537
2023; 60(5): 1321-1334
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd