Minimal Prime Ideals of Ore Extensions over Commutative Dedekind Domains

TL;DR

This paper extends the understanding of minimal prime ideals in Ore extensions over Dedekind domains to cases where the derivation  is non-zero, broadening previous results that only covered the =0 case.

Contribution

It generalizes the characterization of minimal prime ideals in Ore extensions over Dedekind domains to include non-zero derivations , expanding prior work.

Findings

Extended the classification of minimal prime ideals to non-zero derivations

Provided a general framework for Ore extensions over Dedekind domains

Built upon previous results for the =0 case

Abstract

Let R = D[x;\sigma;\delta] be an Ore extension over a commutative Dedekind domain D, where \sigma is an automorphism on D. In the case \delta = 0 Marubayashi et. al. already investigated the class of minimal prime ideals in term of their contraction on the coefficient ring D. In this note we extend this result to a general case \delta not 0.