 Polynomial ring over a unique factorization domain (source code)

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= Polynomial ring over a unique factorization domain

If $R$ is a <unique factorization domain> with fraction field $F$, then $R[X]$ is a unique factorization domain. A primitive polynomial irreducible in $R[X]$ remains irreducible, hence prime, in the principal ideal domain $F[X]$; <Gauss lemma for polynomials> brings divisibility back to $R[X]$.

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