Algebraic number theory MOC

Gauß's lemma

Suppose $𝑅$ is a Unique factorization domain and $𝐹 = F r a c 𝑅$ is its Field of fractions. Then #m/thm/num/alg

The set of primitive polynomials in $𝑅 [𝑥]$ is closed under multuplication;
$𝑓 (𝑥) \in 𝑅 [𝑥]$ is irreducible iff it is irreducible in $𝐹 [𝑥]$ and primitive.

Proof

#missing/proof

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