Lemma 31.26.6 (02RP)—The Stacks project

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Lemma 31.26.6. Let $X$ be a locally Noetherian integral scheme. Let $f, g \in R(X)^*$. Then

\[ \text{div}_ X(fg) = \text{div}_ X(f) + \text{div}_ X(g) \]

as Weil divisors on $X$.

Proof. This is clear from the additivity of the $\text{ord}$ functions. $\square$

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