Definition 1

Tag 0D5V, permanent. Cite it as [Bourbaki, Tag 0D5V].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

One says that a ring $A$ is regular if it is noetherian and if the local ring $A_m$ is regular for every maximal ideal $m$ of $A$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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