Let D be a UFD. , if is not a unit, will there always exists a prime that is the common divisor of ?why?
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Originally Posted by ynj Let D be a UFD. , if is not a unit, will there always exists a prime that is the common divisor of ?why? of course. just choose to be any prime element in the prime factorization of .
prime factoralization? but the definition of UFD says that any nonunit a can be factorlized in to product of irreducible elements, say , where . Do you mean that is prime,or there is other theorem named"prime factoralization"?
oh,sorry, i have just searched the internet, and find a proof which says that irreducible and prime are equivalent in UFD
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