Lemma 3

Tag 008B, permanent. Cite it as [Bourbaki, Tag 008B].

Algebra, VIII, p. 122, § 7. Simple Rings

Let A be a simple ring, and let S be a simple A-module. Denote the opposite field of the commutant of S by D. Every A-module is isomorphic to an A-module of the form $S\otimes_DV$ , where V is a left vector space over the field D.

This follows from Lemma 1 of VIII, p. 120 and Morita’s theorem (VIII, p. 103).

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 2, § 7
Proposition 4, § 7

Cites

VIII, p. 103
Lemma 1 of VIII, p. 120