Lemma 15.104.13. Let $A \to B$ be a ring map such that $B \otimes _ A B \to B$ is flat.

If $A \to B$ is of finite type, then $A \to B$ is unramified.

If $A \to B$ is of finite presentation and flat, then $A \to B$ is étale.

In particular a weakly étale ring map of finite presentation is étale.

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