Locally nilpotent skew extensions of rings

We extend existing results on locally nilpotent differential polynomial rings to skew extensions of rings. We prove that if G={sigma t}(t is an element of T) (i)s a locally finite family of automorphisms of an algebra R, D={dt} t.Tis a family of skew derivations of Rsuch that the prime radical Pof Ris strongly invariant under D, then the ideal P < T, G, D >* of R < T, G, D >, generated by P, is locally nilpotent. We then apply this result to algebras with locally nilpotent derivations. We prove that any algebra Rover a field of characteristic 0, having a surjective locally nilpotent derivation dwith commutative kernel, and such that Ris generated by ker d(2), has a locally nilpotent Jacobson radical. (C) 2020 Elsevier B.V. All rights reserved.