An **atomic domain** is a concept in the field of mathematics, specifically in the area of ring theory, which is a branch of abstract algebra. A domain is a specific type of ring that has certain properties, and an atomic domain is a further classification of such a ring. In general, a **domain** (often referred to as an integral domain) is a commutative ring with no zero divisors and where the multiplication operation is closed.
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An atomic domain is an integral domain in which every nonzero nonunit is a finite product of irreducible elements. Every unique factorization domain is atomic, but atomicity alone does not imply uniqueness.