# PRINC domains and comaximal factorization domains

## TL;DR

This paper explores the properties of PRINC domains, a class of integral domains where two-generated invertible ideals are principal, and investigates their relationship with comaximal factorization domains, revealing that many PRINC domains are not comaximal factorization domains.

## Contribution

The paper demonstrates that large classes of PRINC domains are not comaximal factorization domains and constructs examples of PRINC domains that are neither comaximal factorization domains nor projective-free.

## Key findings

- Many PRINC domains are not comaximal factorization domains
- Constructed examples of PRINC domains that are not comaximal factorization domains
- Produced PRINC domains that are neither comaximal factorization domains nor projective-free

## Abstract

The notion of PRINC domain was introduced by Salce and Zanardo (2014), motivated by the investigation of the products of idempotent matrices with entries in a commutative domain. An integral domain R is a PRINC domain if every two-generated invertible ideal of R is principal. PRINC domains are closely related to the notion of unique comaximal factorization domain, introduced by McAdam and Swan (2004). In this article, we prove that there exist large classes of PRINC domains which are not comaximal factorization domains, using diverse kinds of constructions. We also produce PRINC domains that are neither comaximal factorization domains nor projective-free.