Remark 2

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

Algebra, IV, p. 15, § 2. Zeros of polynomials

Let $B$ be a commutative ring containing $\mathbf{A}$ as subring. Let $f \in \mathbf{A}[X]$ be non-zero and $a \in \mathbf{A}$ . The order of $a$ relative to $f$ is the same, whether we consider $f$ as element of $B[X]$ or as element of $\mathbf{A}[X]$ . This is clear from condition (ii) of Prop. 2.

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

Cited by

Nothing.

Cites

Prop. 2