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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.09515 |
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Table des matières:
- We show that the formal skew Laurent series ring $R = D(\! ( x; σ)\! )$ over a commutative Dedekind domain $D$ with an automorphism $σ$ is a noncommutative Dedekind domain. If $σ$ acts trivially on the ideal class group of $D$, then $K_0(R)$, the Grothendieck group of $R$, is isomorphic to $K_0(D)$. Furthermore, we determine the Krull dimension, the global dimension, the general linear rank, and the stable rank of $R$.