Skew Laurent Series Ring Over a Dedekind Domain
Abstract
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 K0(R), the Grothendieck group of R, is isomorphic to K0(D). Furthermore, we determine the Krull dimension, the global dimension, the general linear rank, and the stable rank of R.
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