Example 2
Tag 000F, permanent. Cite it as [Bourbaki, Tag 000F].
Algebra, VIII, p. 5, § 1. Artinian Modules and Noetherian Modules
Let A be a ring and D a subring of A. Suppose that D is a field and that A is a finite-dimensional left vector space over D. Then the ring A is left Artinian and left Noetherian because every left ideal of A is a D-vector subspace of A. In particular, a finite-dimensional algebra over a commutative field is a ring that is both left and right Artinian and Noetherian.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
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