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arXiv · 1311.3571

Differential poynomial rings over locally nilpotent rings need not be Jacobson radical

Agata Smoktunowicz·Michal Ziembowski
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Abstract

We answer a question by Shestakov on the Jacobson radical in differential polynomial rings. We show that if R is a locally nilpotent ring with a derivation D then R[X;D] need not be Jacobson radical. We also show that J(R[X;D])\cap R is a nil ideal of R in the case where D is a locally nilpotent derivation and R is an algebra over an uncountable field.

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Agata Smoktunowicz, Michal Ziembowski. 2013-11-25. Differential poynomial rings over locally nilpotent rings need not be Jacobson radical. https://arxiv.org/abs/1311.3571

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