Let $k$ be a field, and let $k[x]$ denote the [polynomial ring](/page/Polynomial%20Ring) in one indeterminate over $k$. For every ideal $I \trianglelefteq k[x]$, there exists a polynomial $d \in k[x]$ such that
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\begin{align*}
I = (d).
\end{align*}
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Moreover, if $I \ne (0)$, then there exists a unique monic polynomial $d \in k[x]$ such that