Definition
Let R be an integral domain. If every non-zero non-unit x of R can be written as a product of irreducible elements, R is referred to as an atomic domain. (The product is necessarily finite, since infinite products are not defined in ring theory. Such a product is allowed to involve the same irreducible element more than once as a factor.) Any such expression is called a factorization of x.
Read more about this topic: Atomic Domain
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