Sub-atomic integral domains require that every nonunit divisor of an atomic element is atomic, forming a class between atomic and non-atomic domains.
Lebowitz–Lockard,On domains with properties weaker than atomicity, Comm
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A Weaker Notion of Atomicity in Integral Domains
Sub-atomic integral domains require that every nonunit divisor of an atomic element is atomic, forming a class between atomic and non-atomic domains.