Corollary 2

Tag 0D61, permanent. Cite it as [Bourbaki, Tag 0D61].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

A regular ring is normal, Gorenstein and Macaulay.

In fact, a regular local ring is integrally closed (VIII, $§ 5$ , No. 2, cor. 1 of th. 1), Gorenstein ( $§ 3$ , No. 9, example 4) and Macaulay ( $§ 2$ , No. 5, example 6).

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

Cited by

Nothing.

Cites

Nothing.