Remark

Tag 0AU3, permanent. Cite it as [Bourbaki, Tag 0AU3].

Lie Groups and Lie Algebras, chapter V, Appendix 0. Complements on linear representations

The preceding proposition applies in particular when $A'$ is an $A$ -algebra. In that case, $M^G \otimes_A A'$ is an $A'$ -submodule of $M \otimes_A A'$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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