Definition 31.26.5. Let $X$ be a locally Noetherian integral scheme. Let $f \in R(X)^*$. The *principal Weil divisor associated to $f$* is the Weil divisor

\[ \text{div}(f) = \text{div}_ X(f) = \sum \text{ord}_ Z(f) [Z] \]

where the sum is over prime divisors and $\text{ord}_ Z(f)$ is as in Definition 31.26.3. This makes sense by Lemma 31.26.4.

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