Lemma 27.7.7. Let $X$ be a locally Noetherian scheme. The following are equivalent:

$X$ is normal, and

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

Lemma 27.7.7. Let $X$ be a locally Noetherian scheme. The following are equivalent:

$X$ is normal, and

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

**Proof.**
Omitted. Hint: This is purely topological from Lemma 27.7.6.
$\square$

Your email address will not be published.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 (2)

Comment #276 by BB on

Comment #277 by Aise Johan de Jong on

There are also: