Bull. Korean Math. Soc. 2016; 53(5): 1309-1325
Online first article August 25, 2016 Printed September 30, 2016
https://doi.org/10.4134/BKMS.b150589
Copyright © The Korean Mathematical Society.
Hong Kee Kim, Tai Keun Kwak, Seung Ick Lee, Yang Lee, Sung Ju Ryu, Hyo Jin Sung, and Sang Jo Yun
Gyeongsang National University, Daejin University, Pusan National University, Pusan National University, Pusan National University, Pusan National University, Pusan National University
{This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.}
Keywords: weak nil-symmetric ring, upper and lower nilradicals coincide, zero divisor, symmetric ring, matrix ring, polynomial ring
MSC numbers: 16U80, 16S70
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