Remark
Tag 00JV, permanent. Cite it as [Bourbaki, Tag 00JV].
Algebra, VIII, p. 323, § 16. Other Descriptions of the Brauer Group
By considering tensor products of quaternion algebras, it is possible to construct fields with center K, exponent 2, and arbitrarily large index (cf. VIII, p. 371, Exercises 7 and 8).
Conversely, if K is a finite Galois extension of a -adic field or a field of formal power series over a finite field, then the exponent of a central simple algebra of finite degree over K is equal to its index (VIII, p. 332, Exercise 17, e)).
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.