Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

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.

Insertion-of-factors-property on nilpotent elements

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

Abstract

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