Proposition 13

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

Algebra, VIII, p. 317, § 16. Other Descriptions of the Brauer Group

There exists a unique isomorphism of $K'$ -algebras $\varphi$ from $\mathbf{A}[\mathscr{E}; L]_{(K')}$ to $\mathbf{A}[\mathscr{E}'; L']$ that satisfies the relations

u'(h(\beta )) =\varphi (1\otimes u(\beta )) \tag{36}

for $\beta \in L$ and

v'(h(\gamma )) =\varphi (1\otimes v(\gamma )) \tag{37}

for $\gamma \in \Gamma$ .

The proof follows immediately from the constructions.

The isomorphism $\varphi$ is called canonical.

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

Nothing.