Example

Tag 0D67, permanent. Cite it as [Bourbaki, Tag 0D67].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

Let B be a nonzero integral algebra of finite type over a field K. By VIII, § 2, No. 4, Cor. 1 of Th. 3, there exists a subalgebra A of B isomorphic to a polynomial algebra over K and such that B is a finitely generated A-module. The following properties are equivalent:

(i) the ring B is Macaulay; (ii) the A-module B is projective; (iii) the A-module B is free.

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

Cited by

Nothing.

Cites

Nothing.