Definition 66.48.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{A}$ be a quasi-coherent sheaf of $\mathcal{O}_ X$-algebras. The integral closure of $\mathcal{O}_ X$ in $\mathcal{A}$ is the quasi-coherent $\mathcal{O}_ X$-subalgebra $\mathcal{A}' \subset \mathcal{A}$ constructed in Lemma 66.48.1 above.

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