2015/04/06 by Agata Smoktunowicz, Smoktunowicz, Agata · 1 citation
Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 16N #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1504.01341
openalex publication_date 2015/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.