Example

Tag 048R, permanent. Cite it as [Bourbaki, Tag 048R].

Commutative Algebra, chapter II, § 3. Local rings. Passage from the local to the global

Every local ring is semi-local. Every quotient of a semi-local ring is semi-local. Every finite product of semi-local rings is semi-local.

If A is a Noetherian semi-local ring and B is an A-algebra which is a finitely generated A-module, then B is semi-local (Chapter IV, § 2, no. 5, Corollary 3 to Proposition 9).

Another example, generalizing the construction of the local rings $A_{\mathfrak{p}}$ , is provided by the following proposition:

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

Cited by

Nothing.

Cites

Chapter IV, § 2, no. 5, Corollary 3 to Proposition 9