A unique factorization domain is a commutative ring in which each element can be written as a product of prime elements and a unit.
Unique factorization domains are GCD rings (or domains), but not necessarily Euclidean domains.
This trait is outside the commutative ring hierarchy, because the factorization algorithms are costly. Another reason: in some cases, a deliberate choice should be made by the user, for example to use probabilistic algorithms with a specified probability of failure.
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