Lemma 31.21.3. Let i : Z \to X be an immersion of schemes. Assume X is locally Noetherian. Then i is regular \Leftrightarrow i is Koszul-regular \Leftrightarrow i is H_1-regular \Leftrightarrow i is quasi-regular.
Lemma 31.21.3. Let i : Z \to X be an immersion of schemes. Assume X is locally Noetherian. Then i is regular \Leftrightarrow i is Koszul-regular \Leftrightarrow i is H_1-regular \Leftrightarrow i is quasi-regular.
Proof. Follows immediately from Lemma 31.21.2 and Lemma 31.20.8. \square
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