Corollary 1

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

Algebra, VIII, p. 253, § 14. Central Simple Algebras

Let A be a central simple algebra of finite degree over a separably closed field K. There exists an integer $n\geqslant 1$ such that A is isomorphic to the matrix algebra $\mathbf{M}_n(K)$ .

Indeed, every Galois extension of K is equal to K; it suffices to apply the equivalence of properties (i) and (v) of Theorem 1.

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

§ 15. Brauer Groups

Cites

Theorem 1