On the Jacobson radical of skew polynomial extensions of rings satisfying a polynomial identity

2014/08/21 by Blake W. Madill, Madill, Blake W.
Mathematics · #16N20 (Primary) #16N40 #16R40 #16W25 (Secondary) #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16N20 #msc:16N40 #msc:16R40 #msc:16W25

paper · pdf · doi:10.48550/arxiv.1408.5112

5 pages

openalex publication_date 2014/08/21 · arxiv created 2014/11/16 · arxiv updated 2014/11/18 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let R be a ring satisfying a polynomial identity and let D be a derivation of R. We consider the Jacobson radical of the skew polynomial ring R[x;D] with coefficients in R and with respect to D, and show that J(R[x;D])∩ R is a nil D-ideal. This extends a result of Ferrero, Kishimoto, and Motose, who proved this in the case when R is commutative.

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