Lemma 71.6.8. Let S be a scheme. Let X be an algebraic space over S. Let Z, Y be two closed subspaces of X with ideal sheaves \mathcal{I} and \mathcal{J}. If \mathcal{I}\mathcal{J} defines an effective Cartier divisor D \subset X, then Z and Y are effective Cartier divisors and D = Z + Y.
Proof. By Lemma 71.6.2 this reduces to the case of schemes which is Divisors, Lemma 31.13.9. \square
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