The Stacks project

Definition 31.13.1. Let $S$ be a scheme.

1. A locally principal closed subscheme of $S$ is a closed subscheme whose sheaf of ideals is locally generated by a single element.

2. An effective Cartier divisor on $S$ is a closed subscheme $D \subset S$ whose ideal sheaf $\mathcal{I}_ D \subset \mathcal{O}_ S$ is an invertible $\mathcal{O}_ S$-module.