Remark 1

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

Algebra, VIII, p. 97, § 6. Morita Equivalence of Modules and Algebras

Suppose that the mapping $b\mapsto b_P$ from B to End $_A(P)$ is bijective. Then

a) the B-module P can be identified with the countermodule of P; it is therefore faithful and balanced;

b) the mapping $a\mapsto a_P$ from A to End $_B(P)$ is bijective if and only if the A-module P is faithful and balanced.

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, § 6
Corollary 2, § 6

Cites

Nothing.