I'm currently reading a textbook on algebra, and one of the lemmas is the following:(adsbygoogle = window.adsbygoogle || []).push({});

Let D be a UFD and let F be the field of quotients of D. Let f(x) in D[x] where degree(f(x)) > 0.

If f(x) is irreducible in D[x], then f(x) is also irreducible in F[x].

Also, if f(x) is primitive in D[x] and irreducible in F[x], then f(x) is irreducible in D[x].

It then says that this lemma shows that the irreducibles in D[x] are precisely the irreducibles in D, together with the nonconstant primitive polynomials that are irreducible in F.

Can someone explain how the lemma implies this, in particular it makes no mention of the irreducibles of D.

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# Question on UFDs

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