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| author | Juan Marín Noguera <juan.marinn@um.es> | 2021-06-11 15:15:08 +0200 |
|---|---|---|
| committer | Juan Marín Noguera <juan.marinn@um.es> | 2021-06-11 15:15:08 +0200 |
| commit | ccee3019554dba80c89adf45a6992820299699d4 (patch) | |
| tree | c89a97cd55b785e4d08ff9c2ccc7e40b8d0929bf /ealg/n4.lyx | |
| parent | 84c718bd2189c6d92d8474fc4a4a9ebde12afdee (diff) | |
Cosas que ya no entran
Diffstat (limited to 'ealg/n4.lyx')
| -rw-r--r-- | ealg/n4.lyx | 91 |
1 files changed, 0 insertions, 91 deletions
diff --git a/ealg/n4.lyx b/ealg/n4.lyx index 01a240d..d6843c6 100644 --- a/ealg/n4.lyx +++ b/ealg/n4.lyx @@ -1635,97 +1635,6 @@ Sean \end_inset -isomorfos. - -\series bold -Demostración: -\series default - Si -\begin_inset Formula $\overline{L}$ -\end_inset - - y -\begin_inset Formula $\overline{L'}$ -\end_inset - - son clausuras algebraicas respectivas de -\begin_inset Formula $L$ -\end_inset - - y -\begin_inset Formula $L'$ -\end_inset - -, lo son de -\begin_inset Formula $K$ -\end_inset - - y -\begin_inset Formula $K'$ -\end_inset - - por ser -\begin_inset Formula $K\subseteq L$ -\end_inset - - y -\begin_inset Formula $K'\subseteq L'$ -\end_inset - - algebraicas, y por lo anterior -\begin_inset Formula $\sigma$ -\end_inset - - se extiende a un isomorfismo -\begin_inset Formula $\overline{\sigma}:\overline{L}\to\overline{L'}$ -\end_inset - -. - Tenemos -\begin_inset Formula $L=K(S:=\{\alpha\in\overline{L}:\alpha\text{ es raíz de un }f\in{\cal P}\})$ -\end_inset - - y -\begin_inset Formula $L':=K(S':=\{\alpha'\in\overline{L'}:\alpha'\text{ es raíz de un }f'\in{\cal P}'\})$ -\end_inset - -, pero si un -\begin_inset Formula $\alpha\in S$ -\end_inset - - es raíz de un -\begin_inset Formula $f\in{\cal P}$ -\end_inset - -, entonces -\begin_inset Formula $\overline{\sigma}(\alpha)\in\overline{L'}$ -\end_inset - - es raíz de -\begin_inset Formula $\overline{\sigma}(f)=\sigma(f)\in\sigma({\cal P})={\cal P}'$ -\end_inset - -, luego -\begin_inset Formula $\overline{\sigma}(\alpha)\in S'$ -\end_inset - - y -\begin_inset Formula $\overline{\sigma}(S)\subseteq S'$ -\end_inset - -. - Usando -\begin_inset Formula $\overline{\sigma}^{-1}$ -\end_inset - - se obtiene el otro contenido, luego -\begin_inset Formula $\overline{\sigma}(L)=\overline{\sigma}(K(S))=\overline{\sigma}(K)(\overline{\sigma}(S))=K'(S')=L'$ -\end_inset - - y -\begin_inset Formula $\overline{\sigma}|_{L}:L\to L'$ -\end_inset - -. \end_layout \begin_layout Standard |
