The torsionfree part of the Ziegler spectrum of orders over Dedekind domains

TL;DR

This paper investigates the structure of the torsionfree part of the Ziegler spectrum for orders over Dedekind domains, emphasizing the role of lattices and describing the spectrum in finite lattice representation cases.

Contribution

It provides a detailed description of the torsionfree Ziegler spectrum for orders over Dedekind domains, especially when the order has finite lattice representation type.

Findings

Characterization of the torsionfree part of the spectrum

Role of lattices over orders in Dedekind domains

Explicit description for finite lattice representation type

Abstract

We study the R-torsionfree part of the Ziegler spectrum of an order \Lambda over a Dedekind domain R. We underline and comment on the role of lattices over \Lambda. We describe the torsionfree part of the spectrum when \Lambda is of finite lattice representation type.