2023/01/06 by Adam Jones, Jones, Adam, William G. Woods +1
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2301.02639
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.