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The Stacks project

Lemma 10.36.5. Let R \to S be a ring map. The following are equivalent

  1. R \to S is finite,

  2. R \to S is integral and of finite type, and

  3. there exist x_1, \ldots , x_ n \in S which generate S as an algebra over R such that each x_ i is integral over R.

Proof. Clear from Lemma 10.36.4. \square


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