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

2013/11/14 by Agata Smoktunowicz, Smoktunowicz, Agata, Michal Ziembowski +1
Mathematics · #16N20 #16S36 #16W25 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16N20 #msc:16S36 #msc:16W25

paper · pdf · doi:10.48550/arxiv.1311.3571

arxiv created 2013/11/25 · arxiv updated 2013/11/26

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])∩ 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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