[[Algebraic number theory MOC]]
# Gauß's lemma

Suppose $R$ is a [[Unique factorization domain]] and $F = \Frac R$ is its [[Field of fractions]].
Then #m/thm/num/alg 

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

> [!missing]- Proof
> #missing/proof


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