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

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Filtered skew derivations on simple artinian rings

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月17日

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  • Adam Jones,
  • William Woods

摘要

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.