Definition 2

Tag 0521, permanent. Cite it as [Bourbaki, Tag 0521].

Commutative Algebra, chapter VII, § 3. Factorial domains

A polynomial $F \in \mathbf{A}[X]$ is called distinguished if it is of the form

F = X^s + a_{s-1} X^{s-1} + \cdots + a_0,

where

a_i \in \mathfrak{m}

for

0 \leq i \leq s - 1

Note that the product of two distinguished polynomials is a distinguished polynomial.

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

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