Lemma 27.7.6. Let $X$ be a Noetherian scheme. The following are equivalent:

$X$ is normal, and

$X$ is a finite disjoint union of normal integral schemes.

Lemma 27.7.6. Let $X$ be a Noetherian scheme. The following are equivalent:

$X$ is normal, and

$X$ is a finite disjoint union of normal integral schemes.

**Proof.**
This is a special case of Lemma 27.7.5 because a Noetherian scheme has a Noetherian underlying topological space (Lemma 27.5.5 and Topology, Lemma 5.9.2.
$\square$

Your email address will not be published.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.

## Comments (0)

There are also: