Lemma 15.96.2. Let $R$ be a ring. Let $G$ be a finite group acting on $R$. Let $I \subset R$ be an ideal such that $\sigma (I) \subset I$ for all $\sigma \in G$. Then $R^ G/I^ G \subset (R/I)^ G$ is an integral extension of rings which induces homeomorphisms on spectra and purely inseparable extensions of residue fields.
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.