Remark 2

Tag 00M3, permanent. Cite it as [Bourbaki, Tag 00M3].

Algebra, VIII, p. 368, § 19. Quaternion Algebras

The above applies to the field $\mathbf{R}$ of real numbers. Every $\mathbf{R}$ -algebra of finite degree that is a field is isomorphic to $\mathbf{R},\mathbf{C}$ , or $\mathbf{H}$ .

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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