The Stacks project

Definition 82.13.1. In Situation 82.2.1 let $X/B$ be good. Assume $X$ is integral with $\dim _\delta (X) = n$. Let $f \in R(X)^*$. The principal divisor associated to $f$ is the $(n - 1)$-cycle

defined in Spaces over Fields, Definition 72.6.7. This makes sense because prime divisors have $\delta$-dimension $n - 1$ by Lemma 82.12.1.