Remark 1

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

Algebra, VIII, p. 321, § 16. Other Descriptions of the Brauer Group

If L is an étale algebra over K and G is the automorphism group of L, then it is not always true that the algebra $\mathbf{A}[\mathscr{E}; L]$ is central simple (for example, we can take $L = K^n$ and $G =\mathfrak{S}_n$ ).

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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