Algebra seminar

“On the Jacobson radical of differential polynomial rings. ”

Let R be a ring satisfying a polynomial identity and let D be a derivation of R. We consider the differential polynomial ring R[x;D] and its Jacobson radical J(R[x;D]). We show that J(R[x,D]) = S[x;D] for some nil D-ideal S of R. This extends a result which was previously only known for commutative rings.