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

作者：Smoktunowicz Agata^*; Ziembowski Michal

来源：Journal of Algebra, 2014, 412: 207-217.

DOI：10.1016/j.jalgebra.2014.04.022

• Jacobson radical
• Differential polynomial ring
• Locally nilpotent ring
• Locally nilpotent derivation

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.

• 出版日期2014-8-15