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The results of the preceding section remain valid if the ring of integers and the field of rationals are respectively replaced by any [[unique factorization ___domain]] {{math|''R''}} and its [[field of fractions]] {{math|''K''}}.
This is typically used for proving that a polynomial ring over a unique factorization ___domain,{{clarification needed|date=July 2016|reason=missing words--for proving what about the ring?}} and for factoring [[multivariate polynomial]]s.
===Unique factorization property of polynomial rings===
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