Errata + proposiciones de ejercicios

1 files changed, 201 insertions, 1 deletions

diff --git a/ealg/n6.lyx b/ealg/n6.lyx
index 50e4d95..da24dc8 100644
--- a/ealg/n6.lyx
+++ b/ealg/n6.lyx
@@ -162,6 +162,27 @@ Ejemplos:
 \end_layout
 
 \begin_layout Enumerate
+\begin_inset Formula $K\subseteq K$
+\end_inset
+
+ es normal.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+Los irreducibles en 
+\begin_inset Formula $K$
+\end_inset
+
+ con una raíz en 
+\begin_inset Formula $K$
+\end_inset
+
+ son de grado 1.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
 Si 
 \begin_inset Formula $[L:K]=2$
 \end_inset
@@ -183,7 +204,7 @@ Los irreducibles en
 \begin_inset Formula $\alpha\in L$
 \end_inset
 
- tiene grado 
+ tienen grado 
 \begin_inset Formula $\text{gr}\text{Irr}(\alpha,K)\leq2$
 \end_inset
 
@@ -785,6 +806,103 @@ Que
 
 \end_deeper
 \begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+hspace{2pt}
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Si 
+\begin_inset Formula $K\subseteq L$
+\end_inset
+
+ es normal, 
+\begin_inset Formula $K\subseteq E$
+\end_inset
+
+ lo es si y sólo si 
+\begin_inset Formula $E$
+\end_inset
+
+ es 
+\series bold
+estable
+\series default
+ en 
+\begin_inset Formula $K\subseteq L$
+\end_inset
+
+, es decir, si 
+\begin_inset Formula $\forall\sigma\in\text{Gal}(L/K),\sigma(E)=E$
+\end_inset
+
+.
+ Una extensión 
+\begin_inset Formula $K\subseteq L$
+\end_inset
+
+ es normal si y sólo si existe una extensión 
+\begin_inset Formula $L\subseteq N$
+\end_inset
+
+ con 
+\begin_inset Formula $K\subseteq N$
+\end_inset
+
+ normal y tal que todo 
+\begin_inset Formula $K$
+\end_inset
+
+-encaje de 
+\begin_inset Formula $L$
+\end_inset
+
+ en 
+\begin_inset Formula $N$
+\end_inset
+
+ es un 
+\begin_inset Formula $K$
+\end_inset
+
+-automorfismo de 
+\begin_inset Formula $L$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 Sean 
 \begin_inset Formula $K\subseteq L$
 \end_inset
@@ -1617,6 +1735,88 @@ Si
 
 \end_deeper
 \begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{-0.8em}{
+\backslash
+hbox{
+\backslash
+vline
+\backslash
+vbox{
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+\begin_inset Argument item:1
+status open
+
+\begin_layout Plain Layout
+4.
+\end_layout
+
+\end_inset
+
+Si 
+\begin_inset Formula $p:=\text{car}K\neq0$
+\end_inset
+
+, 
+\begin_inset Formula $K$
+\end_inset
+
+ es perfecto si y sólo si todo 
+\begin_inset Formula $a\in K$
+\end_inset
+
+ tiene una raíz 
+\begin_inset Formula $p$
+\end_inset
+
+-ésima en 
+\begin_inset Formula $K$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Enumerate
+\begin_inset Argument item:1
+status open
+
+\begin_layout Plain Layout
+5.
+\end_layout
+
+\end_inset
+
+Una extensión algebraica de un cuerpo perfecto es perfecta.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 Además:
 \end_layout