Korean J. Math. Vol. 27 No. 1 (2019) pp.141-150
DOI: https://doi.org/10.11568/kjm.2019.27.1.141

On a ring property related to nilradicals

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Published: Mar 30, 2019
Keywords:
equal-nilradical ring, lower nilradical, upper nilradical, Jacobson radical, polynomial ring, matrix ring
Mathematics Subject Classification:
16N40, 16N20, 16S36, 16S50

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Hai-lan Jin
Department of Mathematics, Yanbian University, Yanji 133002, China
Zhelin Piao
Department of Mathematics, Yanbian University, Yanji 133002, China
Sang Jo Yun
Department of Mathematics, Dong-A University, Busan, 49315, Korea

Abstract

In this article we investigate the structure of rings in which lower nilradicals coincide with upper nilradicals. Such rings shall be said to be quasi-2-primal. It is shown first that the K$\ddot{\text{o}}$the's conjecture holds for quasi-2-primal rings. So the results in this article may provide interesting and useful information to the study of nilradicals in various situations. In the procedure we study the structure of quasi-2-primal rings, and observe various kinds of quasi-2-primal rings which do roles in ring theory.


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