Loading [MathJax]/extensions/tex2jax.js

The Stacks project

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

Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0G32. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 10.47.11 as pdf