Corollary 2

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

Algebra, VIII, p. 357, § 18. Simple Algebras over a Finite Field

Let K be a finite commutative field. Every central simple algebra over K is isomorphic to a matrix algebra $\mathbf{M}_n(K)$ , where $n$ is a strictly positive integer.

This follows from Theorem 2 and the structure theorem for central simple algebras (VIII, p. 252, 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
Corollary 1, § 19

Cites

VIII, p. 252, Theorem 1
Theorem 2