Remark 1

Tag 00O2, permanent. Cite it as [Bourbaki, Tag 00O2].

Algebra, VIII, p. 420, § 21. Linear Representations of Finite Groups

Suppose that $K'$ is an extension of $K$ and that the isomorphism $\varphi$ is the mapping $\xi \mapsto \xi \cdot 1$ ; then the mapping $\varphi_G$ is given by extension of scalars from $K$ to $K'$ .

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.

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