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In [[mathematics]], a '''unique factorization ___domain (UFD)''' is, roughly speaking, a [[commutative ring]] in which every element which is not a [[unit (ring theory)|unit]] can be uniquely written as a product of [[prime element]]s, analogous to the [[fundamental theorem of arithmetic]] for the [[integer]]s. UFDs are sometimes called '''factorial rings''', following the terminology of [[Nicolas Bourbaki|Bourbaki]].
Some specific kinds of unique factorization domains are given with the following chain of [[subset|set inclusions]]:
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