The nilpotency of the radical in a finitely generated P.I. ring

AbstractLet R = Λ{x1,…, xk} be a p.i. ring, satisfying a monic polynomial identity (one of its coefficients is ± 1), where Λ is a central noetherian subring. It is proven that N(R), the nil radical of R, is nilpotent. As a corollary, by taking Λ = F, a field, we settle affirmatively the open problem posed in (C. Procesi, “Rings with Polynomial Identities,” p. 186, Marcel Dekker, New York, 1973). We prove: “The Jacobson radical of a finitely generated p.i. algebra is nilpotent.