Bourbaki

Remark

Tag 005R, permanent. Cite it as [Bourbaki, Tag 005R].

Algebra, VIII, p. 83, § 5. Commutation

Let M be an A-module. If the AMA_M-module M is generating, then we have AM=AM′′A_M= A''_M by Theorem 2 applied to the AMA_M-module M, so that M is a balanced A-module.

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

Nothing.

Cites

Transcribed from the printed edition, 2023, Springer Nature. Not translated.