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Classifying Subatomic Domains

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.