Corollary 1

Tag 006X, permanent. Cite it as [Bourbaki, Tag 006X].

Algebra, VIII, p. 99, § 6. Morita Equivalence of Modules and Algebras

The countermodule of a generating module is projective and finitely generated. The countermodule of a finitely generated projective module is generating.

Let A be a $k$ -algebra, and let M be an A-module. We denote the opposite $k$ -algebra of the algebra End $_A(M)$ by B. The corollary follows from Proposition 4 applied to the $(A,B)_k$ -bimodule M.

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.

Cited by

Proposition 4, § 8

Cites

Proposition 4