Lemma 67.48.6 (0AYF)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.48: Relative normalization of algebraic spaces
Lemma 67.48.6 (cite)

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Lemma 67.48.6. Let $S$ be a scheme. Let $f : Y \to X$ be a quasi-compact and quasi-separated morphism of algebraic spaces over $S$. Let $X' \to X$ be the normalization of $X$ in $Y$. If $Y$ is reduced, so is $X'$.

Proof. This follows from the fact that a subring of a reduced ring is reduced. Some details omitted. $\square$

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