Inicio extensiones

2 files changed, 315 insertions, 0 deletions

diff --git a/ealg/n.lyx b/ealg/n.lyx
index 70ac499..12db22d 100644
--- a/ealg/n.lyx
+++ b/ealg/n.lyx
@@ -162,5 +162,19 @@ filename "n1.lyx"
 
 \end_layout
 
+\begin_layout Chapter
+Extensiones de cuerpos
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "n2.lyx"
+
+\end_inset
+
+
+\end_layout
+
 \end_body
 \end_document
diff --git a/ealg/n2.lyx b/ealg/n2.lyx
new file mode 100644
index 0000000..e3050d9
--- /dev/null
+++ b/ealg/n2.lyx
@@ -0,0 +1,301 @@
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass book
+\begin_preamble
+\input{../defs}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children false
+\language spanish
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style french
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+Si 
+\begin_inset Formula $K$
+\end_inset
+
+ es un cuerpo y 
+\begin_inset Formula $A$
+\end_inset
+
+ es un anillo, todo homomorfismo de anillos 
+\begin_inset Formula $h:K\to A$
+\end_inset
+
+ es un isomorfismo 
+\begin_inset Formula $K\to h(K)$
+\end_inset
+
+.
+ En efecto, 
+\begin_inset Formula $\ker h\subseteq K$
+\end_inset
+
+ es un ideal y los únicos ideales de 
+\begin_inset Formula $K$
+\end_inset
+
+ son 0 y 
+\begin_inset Formula $K$
+\end_inset
+
+, pero 
+\begin_inset Formula $1\notin\ker h$
+\end_inset
+
+, luego 
+\begin_inset Formula $\ker h=0$
+\end_inset
+
+, 
+\begin_inset Formula $h$
+\end_inset
+
+ es inyectivo y 
+\begin_inset Formula $h:K\to h(K)$
+\end_inset
+
+ es biyectivo.
+\end_layout
+
+\begin_layout Standard
+Una 
+\series bold
+extensión
+\series default
+ (
+\series bold
+de cuerpos
+\series default
+) es un par de cuerpos 
+\begin_inset Formula $(K,L)$
+\end_inset
+
+ con 
+\begin_inset Formula $K$
+\end_inset
+
+ es subcuerpo de 
+\begin_inset Formula $L$
+\end_inset
+
+, que representamos como 
+\begin_inset Formula $K\subset L$
+\end_inset
+
+, 
+\begin_inset Formula $L/K$
+\end_inset
+
+ o, si 
+\begin_inset Formula $K\neq L$
+\end_inset
+
+, como 
+\begin_inset Formula $K\subsetneq L$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Algunas extensiones son 
+\begin_inset Formula $\mathbb{Q}\subset\mathbb{R}$
+\end_inset
+
+, 
+\begin_inset Formula $\mathbb{R}\subset\mathbb{C}$
+\end_inset
+
+ y, para todo cuerpo 
+\begin_inset Formula $K$
+\end_inset
+
+, 
+\begin_inset Formula $K\subset K(X)$
+\end_inset
+
+, donde 
+\begin_inset Formula $K(X)$
+\end_inset
+
+ es el cuerpo de fracciones de 
+\begin_inset Formula $K[X]$
+\end_inset
+
+.
+ Otras son 
+\begin_inset Formula $\mathbb{Q}\subset\mathbb{Q}[\sqrt{m}]$
+\end_inset
+
+ para 
+\begin_inset Formula $m\in\mathbb{Z}$
+\end_inset
+
+ no cuadrado y 
+\begin_inset Formula $\mathbb{Q}\subset\mathbb{Q}[i]$
+\end_inset
+
+.
+ En ef
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+a.pdf::27
+\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 Standard
+Sea 
+\begin_inset Formula $K$
+\end_inset
+
+ un cuerpo no trivial, existe un subcuerpo 
+\begin_inset Formula $K'$
+\end_inset
+
+ de 
+\begin_inset Formula $K$
+\end_inset
+
+ llamado 
+\series bold
+subcuerpo primo
+\series default
+ de 
+\begin_inset Formula $K$
+\end_inset
+
+ contenido en cualquier subcuerpo de 
+\begin_inset Formula $K$
+\end_inset
+
+, y este es isomorfo a 
+\begin_inset Formula $\mathbb{Z}_{p}$
+\end_inset
+
+ si la característica de 
+\begin_inset Formula $K$
+\end_inset
+
+ es un entero primo 
+\begin_inset Formula $p$
+\end_inset
+
+ o a 
+\begin_inset Formula $\mathbb{Q}$
+\end_inset
+
+ en caso contrario.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+eremember
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document