Theorem 1

Tag 06AW, permanent. Cite it as [Bourbaki, Tag 06AW].

Algebra, IV, p. 16, § 2. Zeros of polynomials

Let $A$ be an integral domain. Given a non-zero element $f$ of $A[X]$ , of degree $n$ , then the sum of the orders of all the roots off in $A$ is $\leq n$ .

This follows immediately from Prop. 5.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Corollary, § 2
Proposition 9, § 2

Cites

Prop. 5