Lemma 10.164.2. Let $R \to S$ be a ring map. Assume that
$R \to S$ is faithfully flat, and
$S$ is reduced.
Then $R$ is reduced.
Lemma 10.164.2. Let $R \to S$ be a ring map. Assume that
$R \to S$ is faithfully flat, and
$S$ is reduced.
Then $R$ is reduced.
Proof. This is clear as $R \to S$ is injective. $\square$
Comments (1)
Comment #873 by Dylan on