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Abstract
A wellknown 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. The main
idea of the proof introduces a new way of embedding differential polynomial
rings into bigger rings, which we name platinum rings, plus a key part of the
proof involves the solution of matrix theorybased problems.
Original language  English 

Pages (fromto)  555608 
Number of pages  47 
Journal  Israel journal of mathematics 
Volume  219 
Issue number  2 
Early online date  12 May 2017 
DOIs  
Publication status  Epub ahead of print  12 May 2017 
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Agata Smoktunowicz
 School of Mathematics  Personal Chair in Algebra
Person: Academic: Research Active