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authorJuan Marín Noguera <juan.marinn@um.es>2021-06-11 15:15:08 +0200
committerJuan Marín Noguera <juan.marinn@um.es>2021-06-11 15:15:08 +0200
commitccee3019554dba80c89adf45a6992820299699d4 (patch)
treec89a97cd55b785e4d08ff9c2ccc7e40b8d0929bf /ealg
parent84c718bd2189c6d92d8474fc4a4a9ebde12afdee (diff)
Cosas que ya no entran
Diffstat (limited to 'ealg')
-rw-r--r--ealg/n4.lyx91
-rw-r--r--ealg/n5.lyx2
2 files changed, 1 insertions, 92 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
diff --git a/ealg/n5.lyx b/ealg/n5.lyx
index 6d812c2..c3f6450 100644
--- a/ealg/n5.lyx
+++ b/ealg/n5.lyx
@@ -1857,7 +1857,7 @@ Si
\end_inset
-ésima primitiva de uno, entonces
-\begin_inset Formula $\mathbb{Q}(\xi_{n})\mathbb{Q}(\xi_{m})=\mathbb{Q}(\xi_{nm})$
+\begin_inset Formula $\mathbb{Q}(\xi_{n},\xi_{m})=\mathbb{Q}(\xi_{nm})$
\end_inset
y