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

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Original languageEnglish
Pages (from-to)207-217
Number of pages11
JournalJournal of Algebra
Publication statusPublished - 15 Aug 2014


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]) boolean AND 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. (C) 2014 Elsevier Inc. All rights reserved.

    Research areas

  • Jacobson radical, Differential polynomial ring, Locally nilpotent ring, Locally nilpotent derivation, DERIVATION TYPE, ORE EXTENSIONS

ID: 17563099