On local orders

Abstract

Let R be a complete local Dedekind domain with quotient field K and let Λ be a local R-order in a separable K-algebra. This paper has two major goals. The first is to describe the local orders such that every uniform R-torsion-free module is tame. The second is to describe the pullback structure of local orders with finite representation type and such that every uniform R-torsion-free module is tame. We acomplish these goals by constructing an “ n-ad” order which is, in a certain sense, a maximal local order. This n-ad order provides new characterizations for finite type.