Identities with a single skew derivation

Let R be a prime ring with extended centroid C and δ, a continuous skew derivation of R. We define the notion of K-polynomials which, in the case that δ is an ordinary derivation, reduces to polynomials of the form xδpn+α1xδpn−1+⋯+αnxδ, where αi∈C. It is shown that all generalized identities with δ are consequences of GPIs of R and an identity in the form ψ(x)=xσmb−bx, where ψ(x) is a K-polynomial of minimal possible order m.