The Stacks project

Lemma 10.151.2. Let $R \to S$ be a ring map. The following are equivalent

  1. $R \to S$ is formally unramified and of finite type, and

  2. $R \to S$ is unramified.

Moreover, also the following are equivalent

  1. $R \to S$ is formally unramified and of finite presentation, and

  2. $R \to S$ is G-unramified.

Proof. Follows from Lemma 10.148.2 and the definitions. $\square$

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