The Stacks project

Lemma 29.44.13. Let $X_ i \to Y$, $i = 1, \ldots , n$ be finite morphisms of schemes. Then $X_1 \amalg \ldots \amalg X_ n \to Y$ is finite too.

Proof. Follows from the algebra fact that if $R \to A_ i$, $i = 1, \ldots , n$ are finite ring maps, then $R \to A_1 \times \ldots \times A_ n$ is finite too. $\square$

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