Corollary 2

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

Algebra, VIII, p. 365, § 19. Quaternion Algebras

Let $(E, s)$ be a Cayley algebra over K such that the K-algebra E is central simple of finite degree $>1$ over K. Then E is isomorphic to a quaternion algebra over K.

Every element $u$ of E satisfies $u^2-T_E(u)u+ N_E(u) = 0$ , so the K-algebra E is isomorphic to a quaternion algebra (Corollary 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

Nothing.

Cites

Corollary 1