Gauss's lemma

Statement
Gauss's lemma states that, in a fact about::unique factorization domain, we have the following:


 * A product of fact about::primitive polynomials is primitive.
 * The content of a product of polynomials is the product of their contents (upto associates).

Applications

 * Unique factorization is polynomial-closed: The polynomial ring over a unique factorization domain is again a unique factorization domain. The proof of this is a direct consequence of Gauss's lemma.