Corollary 2

Tag 04N2, permanent. Cite it as [Bourbaki, Tag 04N2].

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

Let $K$ be a field, $L$ an extension of $K$ and $x, x'$ two elements of $L$ which are conjugate over $K$ (Algebra, Chapter V, § 6, no. 2). If $A$ is a subring of $K$ and $x$ is integral over $A$ , $x'$ is also integral over $A$ .

There exists a $K$ -isomorphism $f$ of $K(x)$ onto $K(x')$ such that $f(x) = x'$ and the elements of $A$ are invariant under $f$ .

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

Cited by

Nothing.

Cites

Algebra, Chapter V, § 6, no. 2