Determinantal divisors of products of matrices over Dedekind domains

TL;DR

This paper establishes necessary and sufficient conditions for the existence of matrices over Dedekind domains with prescribed determinantal divisors for the matrices and their product.

Contribution

It provides a complete characterization of when given lists of ideals can be realized as determinantal divisors of matrices and their product over Dedekind domains.

Findings

Develops necessary and sufficient conditions for matrices with prescribed determinantal divisors

Addresses the existence problem for matrices over Dedekind domains

Contributes to the theory of matrix divisors in algebraic number theory

Abstract

Given three lists of ideals of a Dedekind domain, the question is raised, whether there exist two matrices A and B with entries in the given Dedekind domain, such that the given lists of ideals are the determinantal divisors of A, B, and AB, respectively. To answer this question, necessary and sufficient conditions are developed in this article.