Skew derivations whose invariants satisfy a polynomial identity

Abstract

If σ is an automorphism and δ is a q-skew σ-derivation of a ring R, then the subring of invariants is the set R(δ)={r∈R|δ(r)=0}. The main result of this paper is Theorem. Let R be a prime algebra with a q-skew σ-derivation δ, where δ and σ are algebraic. If R(δ)satisfies a P.I., then R satisfies a P.I. If δ is separable, then we also obtain the following result: Theorem. Let δ be a separable q-skew σ-derivation of an algebra R, where δ and σ are algebraic. (i) (ii)∩ σ When R is a domain, it is necessary to assume neither that σ is algebraic nor that δ is q-skew as we prove Theorem. If R is a domain with an algebraic σ-derivation δ such that R(δ) satisfies a P.I., then R also satisfies a P.I. © 2000 Academic Press.