How far can we go with Amitsur's theorem?

Agata Smoktunowicz

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arXiv · 1504.01341

How far can we go with Amitsur's theorem?

Agata Smoktunowicz

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Abstract

A well-known theorem by S.A. Amitsur shows that the Jacobson radical of the polynomial ring R[x] equals I[x] for some nil ideal I of R. In this paper, however, we show that this is not the case for differential polynomial rings, by proving that there is a ring R which is not nil and a derivation D on R such that the differential polynomial ring R[x; D] is Jacobson radical. We also show that, on the other hand, the Amitsur theorem holds for a differential polynomial ring R[x; D], provided that D is a locally nilpotent derivation and R is an algebra over a field of characteristic p>0.

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Agata Smoktunowicz. 2015-04-06. How far can we go with Amitsur's theorem?. https://arxiv.org/abs/1504.01341

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