reversibility over upper nilradicals
Commun. Korean Math. Soc.
Published online January 20, 2020
Da Woon Jung, Chang Ik Lee, Zhelin Piao, Sung Ju Ryu, Hyo Jin Sung, and Sang Jo Yun
Yanbian University, Pusan National University, Dong-A University
Abstract : The studies of reversible and NI rings have done important roles in noncommutative ring theory.
A ring R shall be called QRUR if ab = 0 for a,b in R implies that ba is contained in the upper nilradical of R, which is a generalization of the NI ring property.
In this article we investigate the structure of QRUR rings and examine the QRUR property of several kinds of ring extensions including matrix rings and polynomial rings.
We also show that if there exists a weakly semicommutative ring but not QRUR then Kothe's conjecture does not hold.
Keywords : QRUR ring, QRPR ring, upper nilradical, reversibile ring, K\"othe's conjecture, NI ring, weakly semicommutative ring
MSC numbers : 16N40, 16U80
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