A note on a characterization theorem for a certain class of domains

TL;DR

This paper simplifies and generalizes a characterization theorem for GMPD domains, a class of domains defined by a specific ideal factorization property, enhancing understanding of their structure.

Contribution

It provides a simplified, more general version of the existing characterization theorem for GMPD domains.

Findings

Simplified the characterization theorem for GMPD domains

Extended the theorem to a more general setting

Clarified the factorization properties of non-invertible ideals

Abstract

We have introduced and studied in [3] the class of Globalized multiplicatively pinched-Dedekind domains (GMPD domains). This class of domains could be characterized by a certain factorization property of the non-invertible ideals, (see [3, Theorem 4]). In this note a simplification of the characterization theorem [3, Theorem 4] is provided in more general form.