Bourbaki

Exercise 1, § 4

Commutative Algebra, X

Let AA be a noetherian local ring. In order that AA be regular, it is necessary and sufficient that one has di⁡A(κA)<+∞\operatorname{di}_A(\kappa_A) < +\infty.

Solution

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Machine translation of the English, by gpt-5-6-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.