Filtered skew derivations on simple artinian rings

Given a complete, positively filtered ring (R, f) and a compatible skew derivation (σ, δ), we may construct its skew power series ring R[[x; σ, δ]]. Due to topological obstructions, even if δ is an inner σ-derivation, in general we cannot “untwist” it, i.e., reparametrise to find a filtered isomorphism R[[x; σ, δ]] ≌ R[[x′; σ]], as might be expected from the theory of skew polynomial rings; similarly when σ is an inner automorphism. We find general conditions under which it is possible to untwist the multiplication data, and use this to analyse the structure of R[[x; σ, δ]] in the simplest case when R is a matrix ring over a (noncommutative) noetherian discrete valuation ring.