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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