Definition 1

Tag 04MU, permanent. Cite it as [Bourbaki, Tag 04MU].

Commutative Algebra, chapter V, § 1. Notion of an integral element

Let $A$ be a ring and $R$ an $A$ -algebra (not necessarily commutative). An element $x \in R$ is called integral over $A$ if it satisfies the equivalent properties ( $E_1$ ), ( $E_{II}$ ), ( $E_{III}$ ) of Theorem 1.

A relation of the form $P(x) = 0$ , where $P$ is a monic polynomial in $A[X]$ is also called an equation of integral dependence with coefficients in $A$ .

Examples

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

Cited by

Nothing.

Cites

Theorem 1