Proposition 2

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

Algebra, VIII, p. 339, § 17. Reduced Norms and Traces

Let $a$ be an element of A and Pc( $a; X$ ) its characteristic polynomial. There exists a unique monic polynomial P in K[X] such that we have Pc( $a; X$ ) $= P(X)^n$ .

A) The uniqueness of P follows from Lemma 2 below.

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

Lemma 2