Lemma 10.47.11 (0G32)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.47: Geometrically irreducible algebras
Lemma 10.47.11 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 10.47.11. Let $K/L/M$ be a tower of fields with $L/M$ geometrically irreducible. Let $x \in K$ be transcendental over $L$ . Then $L(x)/M(x)$ is geometrically irreducible.

Proof. This follows from Lemma 10.47.10 because the fields $L(x)$ and $M(x)$ are purely transcendental extensions of $L$ and $M$ . $\square$

Comments (0)

There are also:

6 comment(s) on Section 10.47: Geometrically irreducible algebras

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment