Unique factorization domain
A unique factorization domain is an integral domain in which an analog of the fundamental theorem of arithmetic holds. More precisely an integral domain is a unique factorization domain if for any element which is not a unit:
- can be written in the form where are (not necessarily distinct) irreducible elements in .
- This representation is unique up to units and reordering, that is if where and are all irreducibles then and there is some permutation of such that for each there is a unit such that .
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