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arXiv · 2412.09515

Skew Laurent Series Ring Over a Dedekind Domain

Daniel Vitas
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Abstract

We show that the formal skew Laurent series ring $R = D(\! ( x; \sigma )\! )$ over a commutative Dedekind domain $D$ with an automorphism $\sigma$ is a noncommutative Dedekind domain. If $\sigma$ 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 $R$.

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Daniel Vitas. 2024-12-12. Skew Laurent Series Ring Over a Dedekind Domain. https://doi.org/10.1016/j.jalgebra.2025.07.022

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