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Justifying the representation of a monic polynomial over a UFD
Let $D$ be a UFD and $f(x) \in D[x]$ be monic. The book I'm reading from claims that $$f(x) = p_1(x)^{e_1} \cdots p_n(x)^{e_n}$$
where $p_i(x)$ are distinct, irreducible, and monic, and $e_i >0$.
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