Filtered skew derivations on simple artinian rings
| Autor: | Jones, Adam, Woods, William |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a complete, positively filtered ring $(R,f)$ and a compatible skew derivation $(\sigma,\delta)$, we may construct its skew power series ring $R[[x;\sigma,\delta]]$. Due to topological obstructions, even if $\delta$ is an \emph{inner} $\sigma$-derivation, in general we cannot ``untwist" it, i.e. reparametrise to find a filtered isomorphism $R[[x; \sigma, \delta]] \cong R[[x'; \sigma]]$, as might be expected from the theory of skew polynomial rings; similarly when $\sigma$ 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 $R[[x;\sigma,\delta]]$ in the simplest case when $R$ is a matrix ring over a (noncommutative) noetherian discrete valuation ring. Comment: 17 pages |
| Databáze: | arXiv |
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