Skew Laurent Series Ring Over a Dedekind Domain

Daniel Vitas

doi:10.1016/j.jalgebra.2025.07.022

paper

Skew Laurent Series Ring Over a Dedekind Domain

arXiv:2412.09515 · doi:10.1016/j.jalgebra.2025.07.022

Abstract

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

20 pages