Skew Laurent Series Ring Over a Dedekind Domain

2024/12/12 by Vitas, Daniel
#16E60 #16N60 #16P40 #19A49 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2412.09515

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.

Related

• ω-Euclidean domain and skew Laurent series rings
• What are discrete valuation rings? What are Dedekind domains?
• Simplicity of noncommutative Dedekind domains
• Commutator products in skew Laurent series division rings
• Linear characters of SL₂ over Dedekind domains