Gauss's Lemma on Unique Factorization Domains
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This theorem requires a proof.
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Theorem
Let $R$ be a unique factorization domain.
Then the ring of polynomials $R \sqbrk X$ is also 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 $R \sqbrk X$ is prime.
etc,
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Source of Name
This entry was named for Carl Friedrich Gauss.
