Remark 3

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

Algebra, VIII, p. 362, § 19. Quaternion Algebras

Let $q$ be an element of F. Then $q$ is nilpotent if and only if its characteristic polynomial is equal to $X^4$ , that is, $T_F(q) = N_F(q) = 0$ ; we then have $q^2= 0$ .

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

Proposition 3, § 19
Proposition 5, § 19

Cites

Nothing.