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http://dx.doi.org/10.4134/BKMS.b150589

A GENERALIZATION OF SYMMETRIC RING PROPERTY  

Kim, Hong Kee (Department of Mathematics and RINS Gyeongsang National University)
Kwak, Tai Keun (Department of Mathematics Daejin University)
Lee, Seung Ick (Department of Mathematics Pusan National University)
Lee, Yang (Department of Mathematics Pusan National University)
Ryu, Sung Ju (Department of Mathematics Pusan National University)
Sung, Hyo Jin (Department of Mathematics Pusan National University)
Yun, Sang Jo (Department of Mathematics Pusan National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1309-1325 More about this Journal
Abstract
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;
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