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We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be $\it NJ$ if it satisfies such property. We prove the following: (i) Kothe's conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If $R$ is an NJ ring, then $R$ is exchange if and only if it is clean; and (iii) A ring $R$ is NJ if and only if so is every (one-sided) corner ring of $R$.
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참고문헌 (33)
참고문헌 신청
S. A. Amitsur / 1956 / Radicals of polynomial rings / Canad. J. Math. 8:355~361
F. W. Anderson / 1974 / Rings and Categories of Modules / Springer-Verlag
R. Antoine / 2008 / Nilpotent elements and Armendariz rings / J. Algebra 319(8):3128~3140
S. S. Bedi / 1980 / Jacobson radical of skew polynomial rings and skew group rings / Israel J. Math. 35(4):327~338
H. Chen / 2016 / Rings in which nilpotents belong to Jacobson radical / An. Stiint Univ. Al. I. Cuza Mat.(N.S) LXII:595~606
F. W. Anderson / 1974 / Rings and Categories of Modules / Springer-Verlag
R. Antoine / 2008 / Nilpotent elements and Armendariz rings / J. Algebra 319(8):3128~3140
S. S. Bedi / 1980 / Jacobson radical of skew polynomial rings and skew group rings / Israel J. Math. 35(4):327~338
H. Chen / 2016 / Rings in which nilpotents belong to Jacobson radical / An. Stiint Univ. Al. I. Cuza Mat.(N.S) LXII:595~606
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