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Jacobson Radical and Nilpotent Elements

허찬|천정수|남순혜
영남수학회 (Youngnam Mathematical Society)|2018.01|East Asian Mathematical Journal|제34권 제1호|pp. 39-46|DOI http://dx.doi.org/10.7858/eamj.2018.005

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키워드

Jacobson Radical and Nilpotent Elements.
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초록

In this article we consider rings whose Jacobson radical con- tains all the nilpotent elements, and call such a ring an NJ-ring. The class of N J -rings contains N I -rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

Abstract

In this article we consider rings whose Jacobson radical con- tains all the nilpotent elements, and call such a ring an NJ-ring. The class of N J -rings contains N I -rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

참고문헌 (17)

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