Domains with invertible-radical factorization

TL;DR

This paper investigates a class of integral domains where each proper ideal factors into an invertible ideal and a product of radical ideals, providing insights into their structural properties.

Contribution

It introduces and characterizes a new class of integral domains based on a specific ideal factorization property involving invertible and radical ideals.

Findings

Characterization of domains with invertible-radical ideal factorizations

Identification of structural properties of these domains

Connections to existing classes of integral domains

Abstract

We study those integral domains in which every proper ideal can be written as an invertible ideal multiplied by a nonempty product of proper radical ideals.