Bounded skew power series rings for inner σ-derivations

We define and explore the bounded skew power series ring R⁺[[x;σ,δ]] defined over a complete, filtered, Noetherian prime ring R with a commuting skew derivation (σ,δ). We establish precise criteria for when this ring is well-defined, and for an appropriate completion Q of $Q(R)$, we prove that if Q has characteristic p, δ is an inner σ-derivation and no positive power of σ is inner as an automorphism of Q, then Q⁺[[x;σ,δ]] is often prime, and even simple under certain mild restrictions on δ. It follows from this result that R⁺[[x;σ,δ]] is itself prime.