Lemma 31.15.9. Let $Z \subset X$ be a closed subscheme of a Noetherian scheme. Assume

$Z$ has no embedded points,

every irreducible component of $Z$ has codimension $1$ in $X$,

every local ring $\mathcal{O}_{X, x}$, $x \in Z$ is a UFD or $X$ is regular.

Then $Z$ is an effective Cartier divisor.

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