Definition 70.6.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$.

A

*locally principal closed subspace*of $X$ is a closed subspace whose sheaf of ideals is locally generated by $1$ element.An

*effective Cartier divisor*on $X$ is a closed subspace $D \subset X$ such that the ideal sheaf $\mathcal{I}_ D \subset \mathcal{O}_ X$ is an invertible $\mathcal{O}_ X$-module.

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