ON THE JACOBSON RADICAL OF SKEW POLYNOMIAL EXTENSIONS OF RINGS SATISFYING A POLYNOMIAL IDENTITY

摘要

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]) boolean AND 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.