Gauss's Lemma (Ring Theory)
From ProofWiki
Theorem
Let $R$ be a unique factorization domain.
Then the Ring of Polynomial Functions $R \left[{X}\right]$ is a unique factorization domain.
Proof
Since a UFD is Noetherian, and a Noetherian Domain is UFD if every irreducible element is prime, it is sufficient to prove that every irreducible element of $R[X]$ is prime.
etc,
$\blacksquare$
this possibly works
You can help Proof Wiki by expanding it.
To discuss it in more detail, feel free to use the talk page.
When this page/section has been completed, {{Stub}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
