Geodesic
On rings radical over commutative subrings
Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 511-520

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The following theorem is proved. If a ring $R$ is radical over a commutative subring $K$, then all the nilpotent elements of $R$ generate a null-ideal $T$ for which the corresponding factor ring is commutative. An affirmative answer is thus provided for a question raised by Faith. Bibliography: 5 titles. 
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     author = {A. I. Likhtman},
     title = {On rings radical over commutative subrings},
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A. I. Likhtman. On rings radical over commutative subrings. Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 511-520. http://geodesic.mathdoc.fr/item/SM_1970_12_4_a1/