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How far can we go with Amitsur's theorem in differential polynomial rings? | | Agata Smoktunowicz
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6 Apr 2015 | | 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. However, in this
paper, 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.
Additionally, we 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. | | Source: | arXiv, 1504.1341 | | Services: | Forum | Review | PDF | Favorites | |
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