Remark 3

Tag 00M4, permanent. Cite it as [Bourbaki, Tag 00M4].

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

Let A be a normed algebra over the field $\mathbf{R}$ . Suppose that A is a field. Then A is isomorphic to $\mathbf{R},\mathbf{C}$ , or $\mathbf{H}$ (“Gelfand–Mazur theorem”) (cf. Comm. Alg., VI, §6, No. 4, p. 407, Theorem 1 and TS, I, §2, n $^o5$ , p. 26, corollaire $2$ ) $.*$

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

Comm. Alg., VI, §6, No. 4, p. 407, Theorem 1 not in this corpus: AC VI
TS, I, §2, n$^o5$, p. 26 not in this corpus: TS I