From c77ba32e816f961cf9cbd8368c125871198af8b4 Mon Sep 17 00:00:00 2001
From: Juan Marín Noguera <juan.marinn@um.es>
Date: Sat, 12 Jun 2021 15:16:21 +0200
Subject: Pruebas ejercicios T2

---
 ealg/n.lyx  |  32 ++++++++
 ealg/n2.lyx | 244 ++++++++++++++++++++++++++++++++++++++++++++++++++++--------
 2 files changed, 243 insertions(+), 33 deletions(-)

(limited to 'ealg')

diff --git a/ealg/n.lyx b/ealg/n.lyx
index f1a6298..90d4bf0 100644
--- a/ealg/n.lyx
+++ b/ealg/n.lyx
@@ -148,6 +148,38 @@ Apuntes de Clase, Tercer Curso del Grado en Matemáticas (Cuarto Curso del
  Departamento de Matemáticas, Universidad de Murcia.
 \end_layout
 
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+Se indican con una barra a la izquierda como esta los resultados que proceden
+ de los ejercicios.
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Chapter
 Polinomios
 \end_layout
diff --git a/ealg/n2.lyx b/ealg/n2.lyx
index 3d07f3b..f25344a 100644
--- a/ealg/n2.lyx
+++ b/ealg/n2.lyx
@@ -2226,6 +2226,67 @@ Sea
 \end_layout
 
 \end_deeper
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+hspace{3pt}
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $K\subseteq L$
+\end_inset
+
+ es algebraica si y sólo si todo subanillo 
+\begin_inset Formula $A$
+\end_inset
+
+ intermedio entre 
+\begin_inset Formula $K$
+\end_inset
+
+ y 
+\begin_inset Formula $L$
+\end_inset
+
+ es un cuerpo, si y sólo si para todo cuerpo intermedio 
+\begin_inset Formula $E$
+\end_inset
+
+, todo 
+\begin_inset Formula $K$
+\end_inset
+
+-endomorfismo en 
+\begin_inset Formula $E$
+\end_inset
+
+ es un automorfismo.
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Extensiones simples
 \end_layout
@@ -2549,6 +2610,22 @@ Si
 \end_layout
 
 \end_deeper
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{samepage}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Ejemplos:
 \end_layout
@@ -2656,6 +2733,22 @@ status open
 \begin_layout Plain Layout
 
 
+\backslash
+end{samepage}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
 \backslash
 vspace{-1ex}
 \backslash
@@ -3780,38 +3873,6 @@ Dada una familia
  [...] con el producto componente a componente.
 \end_layout
 
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-eremember
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-sremember{GyA}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -4461,6 +4522,49 @@ finitamente generada
  es finito.
 \end_layout
 
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+Dada una extensión algebraica 
+\begin_inset Formula $K\subseteq L$
+\end_inset
+
+ y 
+\begin_inset Formula $\alpha_{1},\dots,\alpha_{n}\in L$
+\end_inset
+
+, 
+\begin_inset Formula $K(\alpha_{1},\dots,\alpha_{n})=K[\alpha_{1},\dots,\alpha_{n}]$
+\end_inset
+
+.
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sean 
 \begin_inset Formula $K\subseteq L$
@@ -4574,6 +4678,45 @@ Es un cuerpo, pues para
 .
 \end_layout
 
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+Para todo cuerpo 
+\begin_inset Formula $K$
+\end_inset
+
+, 
+\begin_inset Formula $\overline{K}_{K(X)}=K$
+\end_inset
+
+.
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Un 
 \series bold
@@ -4882,7 +5025,26 @@ estable por levantamientos
 \end_inset
 
  también.
- Son estables por levantamientos:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{samepage}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Son estables por levantamientos:
 \end_layout
 
 \begin_layout Enumerate
@@ -4966,6 +5128,22 @@ status open
 \begin_layout Plain Layout
 
 
+\backslash
+end{samepage}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
 \backslash
 hbox{
 \backslash
-- 
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