Proposition 1
Tag 0D7Q, permanent. Cite it as [Bourbaki, Tag 0D7Q].
Commutative Algebra, chapter X, § 6. Extension des scalaires dans les algèbres régulières
If the ring is noetherian, every -algebra essentially of finite type is a noetherian ring.
This follows from III, § 2, No. 10, Cor. 3 of Th. 2 and II, § 2, No. 4, Cor. 2 of Prop. 10.
The following properties are deduced from the definition:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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