Definition 71.6.1. 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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