One-sided duo property on nilpotents

Authors : Chan Yong HONG, Hong Kee KİM, Nam Kyun KİM, Tai Keun KWAK, Yang LEE

Pages : 1974-1987

Doi:10.15672/hujms.571016

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Publication Date : 2020-12-08

Article Type : Research Paper

Abstract :We study the structure of nilpotents in relation with a ring property that is near to one-sided  duo rings. Such a property is said to be one-sided nilpotent-duo. We prove the following for a one-sided nilpotent-duo  ring $R$: insert ignore into journalissuearticles values(i); The set of nilpotents in $R$ forms a subring; insert ignore into journalissuearticles values(ii); Köthe`s conjecture holds for $R$; insert ignore into journalissuearticles values(iii); the subring generated by the identity and the set of nilpotents in $R$ is a  one-sided  duo ring; insert ignore into journalissuearticles values(iv); if the polynomial ring $R[x]$ over $R$ is  one-sided  nilpotent-duo then the set of nilpotents in $R$ forms a commutative ring, and $R[x]$ is an NI ring.  Several connections between  one-sided  nilpotent-duo and  one-sided duo are given. The structure of one-sided nilpotent-duo rings is also studied in various situations in ring theory. Especially we investigate several kinds of conditions under which  one-sided  nilpotent-duo rings are NI.
Keywords : right left, nilpotent duo ring, nilpotent, right left, duo ring, radical, NI ring, matrix ring, ascending chain condition on left insert ignore into journalissuearti