Lemma 72.6.8. Let $S$ be a scheme. Let $X$ be a locally Noetherian integral algebraic space over $S$. Let $f, g \in R(X)^*$. Then

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

as Weil divisors on $X$.

Lemma 72.6.8. Let $S$ be a scheme. Let $X$ be a locally Noetherian integral algebraic space over $S$. 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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