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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