Definition 29.53.2. Let X be a scheme. 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 29.53.1 above.
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