Kaplansky/Nagata-type theorems for the half factorial domains

TL;DR

This paper extends classical Kaplansky and Nagata theorems to the setting of half factorial domains within atomic domains, providing new structural insights.

Contribution

It introduces Kaplansky/Nagata-type theorems specifically for half factorial domains in the context of atomic domains, a novel generalization.

Findings

Characterization of half factorial domains within atomic domains

Extension of classical theorems to new algebraic structures

Structural properties of these domains clarified

Abstract

We give Kaplansky/Nagata-type theorems for the half factorial domains inside the class of atomic domains.