Classifying Subatomic Domains

TL;DR

This paper explores and classifies various subatomic properties in ring theory, demonstrating that these properties are all distinct, thereby extending the understanding of factorization concepts weaker than atomicity.

Contribution

It provides a comprehensive classification of subatomic properties in ring theory, establishing their distinctness and expanding the framework beyond atomic rings.

Findings

All subatomic properties are shown to be distinct.

The paper extends the concept of atomicity to weaker properties.

It clarifies the relationships among various subatomic properties.

Abstract

In general, ring theory is focused on atomic rings, i.e. rings in which every element has some factorization into irreducible elements. In a recent paper of Boynton and Coykendall \cite{BC}, the two authors introduce two properties that are slightly weaker than atomicity, which they call "almost atomicity" and "quasiatomicity". In this paper, we classify various subatomic properties and show that they are all distinct.