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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1970 Volume 83(125), Number 4(12), Pages 513–523 (Mi sm3525)

On rings radical over commutative subrings

A. I. Likhtman


Abstract: 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.

UDC: 519.48

MSC: 13A10, 16N40, 16N20, 16N60

Received: 09.12.1969


 English version:
Mathematics of the USSR-Sbornik, 1970, 12:4, 511–520

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© Steklov Math. Inst. of RAS, 2025