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

Hai-lan Jin, Zhelin Piao, Sang Jo Yun

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.

Keywords


equal-nilradical ring, lower nilradical, upper nilradical, Jacobson radical, polynomial ring, matrix ring

Subject classification

16N40, 16N20, 16S36, 16S50

Sponsor(s)



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