Intrinsic factorization of ideals in Dedekind domains

TL;DR

This paper generalizes polynomial factorization algorithms to ideals in Dedekind domains, providing an intrinsic method that does not rely on specific embeddings, thus broadening the scope of ideal factorization techniques.

Contribution

It introduces an intrinsic ideal factorization algorithm in Dedekind domains, independent of polynomial embeddings, extending existing methods to a more general setting.

Findings

Algorithm successfully factors ideals in Dedekind domains.

Method is intrinsic and does not depend on polynomial embeddings.

Applicable to maximal orders in global function fields.

Abstract

We present a generalization of a polynomial factorization algorithm that works with ideals in maximal orders of global function fields. The method presented in this paper is intrinsic in the sense that it does not depend on the embedding of the ring of polynomials into the Dedekind domain in question.