Comentadas demostraciones que no entran de GyA

3 files changed, 1050 insertions, 464 deletions

diff --git a/ga/n1.lyx b/ga/n1.lyx
index 8457ada..94f9570 100644
--- a/ga/n1.lyx
+++ b/ga/n1.lyx
@@ -349,10 +349,10 @@ Ejemplos:
 \end_inset
 
  son grupos abelianos.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 La suma es asociativa y conmutativa con elemento neutro 0, y todo elemento
  
 \begin_inset Formula $a$
@@ -369,7 +369,11 @@ La suma es asociativa y conmutativa con elemento neutro 0, y todo elemento
  solo el 0 tiene opuesto.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\mathbb{N}$
 \end_inset
@@ -391,15 +395,19 @@ La suma es asociativa y conmutativa con elemento neutro 0, y todo elemento
 \end_inset
 
  son monoides conmutativos con el producto.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 El producto es asociativo y conmutativo con neutro 1, pero el 0 nunca tiene
  opuesto.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Llamamos 
 \begin_inset Formula $Y^{X}$
@@ -423,10 +431,10 @@ Llamamos
 \end_inset
 
  es un monoide, pero no es conmutativo si hay al menos dos elementos.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Claramente 
 \begin_inset Formula $\circ$
 \end_inset
@@ -471,7 +479,11 @@ Claramente
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Llamamos 
 \series bold
@@ -499,14 +511,18 @@ grupo simétrico
 \end_inset
 
  es un grupo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Es asociativa, tiene como neutro la identidad y todo elemento es invertible.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Sea 
 \begin_inset Formula $X$
@@ -530,10 +546,10 @@ Sea
 
  es un monoide conmutativo cuyos elementos invertibles son las funciones
  que no se anulan.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Ambas operaciones son conmutativas y asociativas, la suma tiene como neutro
  la función constante 0 y el producto la función constante 1.
  El inverso de una función 
@@ -563,7 +579,11 @@ Ambas operaciones son conmutativas y asociativas, la suma tiene como neutro
  no se anula.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dada una operación 
 \begin_inset Formula $*$
@@ -605,17 +625,21 @@ Si
 \end_inset
 
  tiene a lo sumo un neutro.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f=e*f=e$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dado un monoide 
 \begin_inset Formula $(X,*)$
@@ -655,17 +679,21 @@ Si
 \end_inset
 
  tiene a lo sumo un simétrico.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $y=e*y=(x*a)*y=x*(a*y)=x*e=x$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $a$
@@ -673,10 +701,10 @@ Si
 
  tiene simétrico por un lado, es cancelable por dicho lado.
  En particular, todo elemento invertible es cancelable.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si, por ejemplo, 
 \begin_inset Formula $a$
 \end_inset
@@ -696,7 +724,11 @@ Si, por ejemplo,
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Anillos
 \end_layout
@@ -979,10 +1011,10 @@ Todo elemento invertible es regular.
 
 .
  En particular, el 0 y el 1 son únicos.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $b+a=a\implies b=b+(a-a)=(b+a)-a=a-a=0$
 \end_inset
 
@@ -993,7 +1025,11 @@ Todo elemento invertible es regular.
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 El opuesto de 
 \begin_inset Formula $a$
@@ -1011,10 +1047,10 @@ El opuesto de
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $0a+0a=(0+0)a=0a=0a+0\implies0a=0$
 \end_inset
 
@@ -1025,16 +1061,20 @@ El opuesto de
  se prueba análogamente.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $a(-b)=(-a)b=-(ab)$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a(-b)+ab=a(-b+b)=a0=0$
 \end_inset
 
@@ -1058,23 +1098,31 @@ El opuesto de
  se prueba análogamente.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $a(b-c)=ab-ac$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a(b-c)=a(b+(-c))=ab+a(-c)=ab+(-ac)=ab-ac$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $a$
 \end_inset
@@ -1096,9 +1144,9 @@ El opuesto de
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1119,6 +1167,7 @@ Basta ver que
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1169,6 +1218,11 @@ Tenemos
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $0=1$
@@ -1179,17 +1233,21 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a\in A\implies a=a1=a0=0$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dado un anillo 
 \begin_inset Formula $A$
@@ -1278,10 +1336,10 @@ Propiedades: Dados un anillo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $n=0$
 \end_inset
@@ -1315,16 +1373,20 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $(n+m)a=na+ma$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $m=0$
 \end_inset
@@ -1358,16 +1420,20 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $n(ma)=(nm)a$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $n=0$
 \end_inset
@@ -1392,7 +1458,11 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $n,m\geq0$
@@ -1415,10 +1485,10 @@ Si
 \end_inset
 
  enteros arbitrarios.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $m=0$
 \end_inset
@@ -1453,7 +1523,7 @@ Para
  
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 Primero vemos que, para 
 \begin_inset Formula $m>0$
 \end_inset
@@ -1502,7 +1572,7 @@ Primero vemos que, para
 .
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 Con esto, sea 
 \begin_inset Formula $m>0$
 \end_inset
@@ -1518,7 +1588,11 @@ Con esto, sea
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $A$
@@ -1545,10 +1619,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $n=0$
 \end_inset
@@ -1586,7 +1660,11 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Subanillos
 \end_layout
@@ -1769,7 +1847,8 @@ Para que
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $[1\implies2]$
@@ -1862,6 +1941,11 @@ Para que
 , luego es cerrado para sumas.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Algunos subanillos:
 \end_layout
@@ -1915,9 +1999,9 @@ Cada uno de
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1950,6 +2034,7 @@ Si
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1967,6 +2052,11 @@ Obvio.
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Llamamos 
 \series bold
@@ -1985,10 +2075,10 @@ subanillo primo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Claramente 
 \begin_inset Formula $\mathbb{Z}1$
 \end_inset
@@ -2039,7 +2129,11 @@ Claramente
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $A$
@@ -2062,14 +2156,18 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 No contiene al 1.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Dado 
 \begin_inset Formula $z\in\mathbb{C}$
@@ -2277,49 +2375,61 @@ Propiedades: Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $0+f(0)=f(0)=f(0+0)=f(0)+f(0)\implies0=f(0)$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(-a)=-f(a)$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f(a)+f(-a)=f(a+(-a))=f(0)=0$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a-b)=f(a)-f(b)$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f(a-b)=f(a)+f(-b)=f(a)-f(b)$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a_{1}+\dots+a_{n})=f(a_{1})+\dots+f(a_{n})$
 \end_inset
@@ -2332,10 +2442,10 @@ Propiedades: Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $n=0$
 \end_inset
@@ -2347,7 +2457,11 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $a$
@@ -2362,10 +2476,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f(a)f(a^{-1})=f(aa^{-1})=f(1)=1$
 \end_inset
 
@@ -2376,7 +2490,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a_{1}\cdots a_{n})=f(a_{1})\cdots f(a_{n})$
 \end_inset
@@ -2402,10 +2520,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $1=f(1)\in f(A')$
 \end_inset
 
@@ -2437,7 +2555,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $B'$
@@ -2456,10 +2578,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $1\in f^{-1}(1)\in f^{-1}(B')$
 \end_inset
 
@@ -2491,7 +2613,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $f$
@@ -2502,10 +2628,10 @@ Si
 \end_inset
 
  también.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f^{-1}(1)=1$
 \end_inset
 
@@ -2545,7 +2671,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Ejemplos:
 \end_layout
@@ -2572,9 +2702,9 @@ Dados anillos
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -2595,6 +2725,7 @@ status open
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -2624,6 +2755,11 @@ status open
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Sea 
 \begin_inset Formula $B$
@@ -2662,10 +2798,10 @@ Dado un anillo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $\mu(1)=1$
 \end_inset
 
@@ -2701,7 +2837,11 @@ Dado un anillo
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Dada una familia de anillos 
 \begin_inset Formula $(A_{i})_{i\in I}$
@@ -2810,7 +2950,12 @@ ideal
 \end_inset
 
 .
- Todo ideal contiene al 0, pues tomando 
+ Todo ideal contiene al 0
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+, pues tomando 
 \begin_inset Formula $a\in I$
 \end_inset
 
@@ -2818,6 +2963,11 @@ ideal
 \begin_inset Formula $0=a+(-1)a\in I$
 \end_inset
 
+
+\end_layout
+
+\end_inset
+
 .
  
 \end_layout
@@ -2905,10 +3055,10 @@ ideal principal
 \end_inset
 
  son de esta forma.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sea 
 \begin_inset Formula $I$
 \end_inset
@@ -2984,7 +3134,11 @@ Sea
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Sean 
 \begin_inset Formula $I$
@@ -3092,7 +3246,11 @@ anillo cociente de
 
 \series default
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -3173,6 +3331,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Es claro que 
 \begin_inset Formula $A/0\cong A$
@@ -3192,7 +3355,11 @@ Es claro que
 \end_inset
 
 .
- En efecto, dado 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, dado 
 \begin_inset Formula $a\in\mathbb{Z}$
 \end_inset
 
@@ -3217,12 +3384,17 @@ Es claro que
 \end_inset
 
 , 
-\begin_inset Formula $a\equiv b\iff a-b\in n\mathbb{Z}\iff n|a-b\overset{|a-b|<n}{\iff}a=b$
+\begin_inset Formula $a\equiv b\iff a-b\in n\mathbb{Z}\iff n\mid a-b\overset{|a-b|<n}{\iff}a=b$
 \end_inset
 
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dado un anillo conmutativo 
 \begin_inset Formula $A$
@@ -3240,9 +3412,9 @@ Dado un anillo conmutativo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3267,6 +3439,7 @@ Dado
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3296,6 +3469,11 @@ En particular
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Un ideal 
 \begin_inset Formula $I$
@@ -3318,9 +3496,9 @@ Un ideal
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[1\implies2\implies3]$
 \end_inset
@@ -3328,6 +3506,7 @@ Un ideal
  Obvio.
 \end_layout
 
+\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[3\implies1]$
 \end_inset
@@ -3356,6 +3535,11 @@ Un ideal
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sea 
 \begin_inset Formula $f:A\to B$
@@ -3391,7 +3575,11 @@ núcleo
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -3472,6 +3660,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Un homomorfismo de anillos 
 \begin_inset Formula $f:A\to B$
@@ -3482,7 +3675,8 @@ Un homomorfismo de anillos
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Itemize
 \begin_inset Argument item:1
@@ -3548,6 +3742,11 @@ Sean
  es inyectiva.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
@@ -3947,7 +4146,11 @@ Sean
 \end_inset
 
 .
- En efecto, 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, 
 \begin_inset Formula $(n)(m)=(\{ab\}_{a\in(n),b\in(m)})=(\{pnqm\}_{p,q\in\mathbb{Z}})=(\{knm\})_{k\in\mathbb{Z}}=(nm)$
 \end_inset
 
@@ -3962,6 +4165,11 @@ Sean
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Teoremas de isomorfía
 \end_layout
@@ -4110,6 +4318,11 @@ Así, si
 \begin_inset Formula $\frac{A\times B}{0\times B}\cong A$
 \end_inset
 
+
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
 , pues el homomorfismo de proyección 
 \begin_inset Formula $f:A\times B\to A$
 \end_inset
@@ -4122,6 +4335,11 @@ Así, si
 \begin_inset Formula $0\times B$
 \end_inset
 
+
+\end_layout
+
+\end_inset
+
 .
 \end_layout
 
@@ -4421,7 +4639,8 @@ característica
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $[1\implies2]$
@@ -4592,6 +4811,11 @@ característica
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
diff --git a/ga/n2.lyx b/ga/n2.lyx
index 4216f33..6bdbc01 100644
--- a/ga/n2.lyx
+++ b/ga/n2.lyx
@@ -130,9 +130,9 @@ subcuerpo
 \end_inset
 
  es inyectivo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[1\implies2]$
 \end_inset
@@ -164,6 +164,7 @@ subcuerpo
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[2\implies1]$
 \end_inset
@@ -246,6 +247,11 @@ subcuerpo
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Un elemento 
 \begin_inset Formula $a\in A$
@@ -256,9 +262,9 @@ Un elemento
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -279,6 +285,7 @@ status open
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -320,6 +327,11 @@ Si
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset CommandInset label
 LatexCommand label
@@ -336,24 +348,28 @@ name "enu:char-domain"
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Consecuencia de lo anterior.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Todo subanillo de un dominio es un dominio.
 \end_layout
 
 \begin_layout Enumerate
 La característica de un dominio no trivial es 0 o un número primo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si la característica de 
 \begin_inset Formula $A$
 \end_inset
@@ -412,9 +428,6 @@ noprefix "false"
 
 \end_layout
 
-\end_deeper
-\begin_layout Standard
-\begin_inset Newpage pagebreak
 \end_inset
 
 
@@ -457,9 +470,9 @@ Para
 \end_inset
 
  es primo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[1\implies3]$
 \end_inset
@@ -475,6 +488,7 @@ Para
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[3\implies2]$
 \end_inset
@@ -522,6 +536,11 @@ Para
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $m\in\mathbb{Z}$
@@ -536,10 +555,10 @@ Si
 \end_inset
 
  es cuerpo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Ambos son subanillos de 
 \begin_inset Formula $\mathbb{C}$
 \end_inset
@@ -617,20 +636,28 @@ Ambos son subanillos de
 
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Un producto de anillos no triviales nunca es un dominio.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $(1,0)(0,1)=(0,0)$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Ideales maximales y primos
 \end_layout
@@ -688,9 +715,9 @@ name "enu:char-maximal"
 \end_inset
 
  es un cuerpo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -747,6 +774,7 @@ Si
 
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -792,6 +820,11 @@ Los únicos ideales de
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset CommandInset label
 LatexCommand label
@@ -808,9 +841,9 @@ name "enu:char-prime"
 \end_inset
 
  es un dominio.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -847,6 +880,7 @@ Sean
  es un dominio.
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -892,16 +926,21 @@ Sean
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $I$
 \end_inset
 
  es maximal, es primo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si es maximal, 
 \begin_inset Formula $A/I$
 \end_inset
@@ -913,16 +952,20 @@ Si es maximal,
  es primo.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $A$
 \end_inset
 
  es cuerpo si y sólo si 0 es maximal.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $A\cong A/0$
 \end_inset
 
@@ -939,16 +982,20 @@ noprefix "false"
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $A$
 \end_inset
 
  es dominio si y sólo si 0 es primo.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $A\cong A/0$
 \end_inset
 
@@ -965,7 +1012,11 @@ noprefix "false"
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dado un conjunto 
 \begin_inset Formula $S$
@@ -998,7 +1049,11 @@ lema de Zorn:
 
 \begin_layout Standard
 Todo ideal propio de un anillo está contenido en un ideal maximal.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1096,6 +1151,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Divisibilidad
 \end_layout
@@ -1229,10 +1289,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sea 
 \begin_inset Formula $x$
 \end_inset
@@ -1252,7 +1312,11 @@ Sea
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dos elementos 
 \begin_inset Formula $a,b\in A$
@@ -1280,22 +1344,6 @@ asociados
 \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
 Si 
 \begin_inset Formula $D$
 \end_inset
@@ -1321,7 +1369,8 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Itemize
 \begin_inset Argument item:1
@@ -1416,17 +1465,6 @@ Claramente
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-end{samepage}
-\end_layout
-
 \end_inset
 
 
@@ -1478,7 +1516,11 @@ Si
 \end_inset
 
  es un dominio, todo primo es irreducible.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1555,9 +1597,18 @@ Demostración:
  es análogo.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Irreducible en un dominio no implica primo.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1648,6 +1699,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sean 
 \begin_inset Formula $A$
@@ -1679,9 +1735,9 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[1\implies2]$
 \end_inset
@@ -1713,6 +1769,7 @@ Sean
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Description
 \begin_inset Formula $[2\implies3\implies1]$
 \end_inset
@@ -1721,6 +1778,11 @@ Sean
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $a$
 \end_inset
@@ -1749,10 +1811,10 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a$
 \end_inset
 
@@ -1799,7 +1861,11 @@ traduciendo
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $A$
@@ -1826,9 +1892,9 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1894,6 +1960,7 @@ Como
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1977,6 +2044,11 @@ Como
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dados un anillo conmutativo 
 \begin_inset Formula $A$
@@ -2064,10 +2136,10 @@ mínimo común múltiplo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a$
 \end_inset
 
@@ -2104,7 +2176,11 @@ mínimo común múltiplo
  Juntando ambos se obtiene el resultado.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $a=\text{mcm}S$
 \end_inset
@@ -2131,10 +2207,10 @@ mínimo común múltiplo
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a$
 \end_inset
 
@@ -2167,7 +2243,11 @@ mínimo común múltiplo
  Juntando ambos se obtiene el resultado.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $a=\text{mcd}S$
@@ -2190,15 +2270,19 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Se obtiene de la caracterización de máximo común divisor y la de asociados
  por ideales principales.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $a=\text{mcm}S$
@@ -2221,14 +2305,18 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Análogo.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset CommandInset label
 LatexCommand label
@@ -2274,10 +2362,10 @@ identidad de Bézout
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $b\in A$
 \end_inset
@@ -2293,7 +2381,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\text{mcd}S=1$
 \end_inset
@@ -2307,9 +2399,9 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -2339,6 +2431,7 @@ Si hubiera un divisor común
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -2360,6 +2453,11 @@ status open
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $1\in(S)$
@@ -2370,10 +2468,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Basta aplicar 
 \begin_inset CommandInset ref
 LatexCommand ref
@@ -2387,7 +2485,11 @@ noprefix "false"
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Dominios de factorización única
 \end_layout
@@ -2534,10 +2636,10 @@ Dado
 \end_inset
 
  es un DF.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $m$
 \end_inset
@@ -2620,6 +2722,7 @@ Si
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -2652,7 +2755,7 @@ Si
 .
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 Sea ahora 
 \begin_inset Formula $x=a+b\sqrt{m}\neq0$
 \end_inset
@@ -2753,6 +2856,11 @@ Sea ahora
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Un dominio 
 \begin_inset Formula $D$
@@ -3053,13 +3161,6 @@ Un dominio
  Por tanto las factorizaciones iniciales son equivalentes.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage pagebreak
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 Dominios de ideales principales
 \end_layout
@@ -3324,10 +3425,10 @@ El cuadrado del módulo complejo es una función euclídea en
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $x:=a+bi$
 \end_inset
@@ -3415,7 +3516,11 @@ Si
 
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sean 
 \begin_inset Formula $\delta$
@@ -3442,7 +3547,8 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Itemize
 \begin_inset Argument item:1
@@ -3582,12 +3688,22 @@ Sea
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Como 
 \series bold
 teorema
 \series default
-, todo dominio euclídeo es DIP, pues si 
+, todo dominio euclídeo es DIP
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+, pues si 
 \begin_inset Formula $\delta$
 \end_inset
 
@@ -3611,6 +3727,11 @@ teorema
 \begin_inset Formula $I=(a)$
 \end_inset
 
+
+\end_layout
+
+\end_inset
+
 .
 \end_layout
 
@@ -3636,7 +3757,8 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $[1\iff3]$
@@ -3683,6 +3805,11 @@ Si
  Obvio.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Cuerpos de fracciones
 \end_layout
@@ -3747,7 +3874,11 @@ Llamamos
 \end_inset
 
 están bien definidas.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -3788,6 +3919,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Propiedades: 
 \begin_inset Formula $\forall a,b\in D;s,t\in D\setminus\{0\}$
@@ -3801,81 +3937,101 @@ Propiedades:
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $\frac{a}{s}=\frac{0}{1}\iff a=a1=s0=0$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\frac{a}{s}=\frac{1}{1}\iff a=s$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $\frac{a}{s}=\frac{1}{1}\iff a=a1=s1=s$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\frac{at}{st}=\frac{a}{s}$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $ats=ast$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\frac{a}{s}=\frac{b}{s}\iff a=b$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $\frac{a}{s}=\frac{b}{s}\iff as=bs\overset{s\neq0}{\iff}a=b$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\frac{a}{s}+\frac{b}{s}=\frac{a+b}{s}$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $\frac{a}{s}+\frac{b}{s}=\frac{as+bs}{ss}=\frac{(a+b)s}{ss}=\frac{a+b}{s}$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 De aquí, 
 \begin_inset Formula $(Q(D),+,\cdot)$
@@ -3902,7 +4058,11 @@ de cocientes
 \end_inset
 
  .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \end_layout
@@ -3970,6 +4130,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Así, 
 \begin_inset Formula $\mathbb{Q}$
@@ -4049,10 +4214,10 @@ Propiedad universal del cuerpo de fracciones:
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $\hat{f}:Q(D)\to K$
 \end_inset
@@ -4102,7 +4267,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Sean 
 \begin_inset Formula $K$
@@ -4121,10 +4290,10 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 El homomorfismo 
 \begin_inset Formula $f:=g\circ u=h\circ u$
 \end_inset
@@ -4152,7 +4321,11 @@ El homomorfismo
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Sean 
 \begin_inset Formula $F$
@@ -4187,10 +4360,10 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Por la Propiedad Universal de 
 \begin_inset Formula $Q(D)$
 \end_inset
@@ -4236,7 +4409,11 @@ Por la Propiedad Universal de
  triviales, es el isomorfismo buscado.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sean 
 \begin_inset Formula $D$
@@ -4259,7 +4436,11 @@ Sean
 \end_inset
 
 .
- En efecto, por la propiedad universal, existe un homomorfismo 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, por la propiedad universal, existe un homomorfismo 
 \begin_inset Formula $\tilde{f}:Q(D)\to K$
 \end_inset
 
@@ -4278,6 +4459,11 @@ Sean
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 De aquí, para 
 \begin_inset Formula $m\in\mathbb{Z}$
@@ -4296,7 +4482,11 @@ De aquí, para
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -4357,6 +4547,11 @@ y recíprocamente,
 
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sea 
 \begin_inset Formula $K$
@@ -4399,7 +4594,11 @@ subcuerpo primo
 \end_inset
 
  en caso contrario.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -4491,5 +4690,10 @@ Demostración:
  
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \end_body
 \end_document
diff --git a/ga/n3.lyx b/ga/n3.lyx
index 772b2a5..f592c64 100644
--- a/ga/n3.lyx
+++ b/ga/n3.lyx
@@ -269,10 +269,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sean 
 \begin_inset Formula $P=:\sum_{k}a_{k}X^{k}$
 \end_inset
@@ -353,6 +353,7 @@ Si la desigualdad es estricta,
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -382,6 +383,11 @@ El coeficiente de grado
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $\text{gr}(PQ)\leq\text{gr}(P)+\text{gr}(Q)$
 \end_inset
@@ -391,10 +397,10 @@ El coeficiente de grado
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $N>n+m$
 \end_inset
@@ -418,7 +424,7 @@ Para
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 El coeficiente de grado 
 \begin_inset Formula $n+m$
 \end_inset
@@ -434,7 +440,11 @@ El coeficiente de grado
 , luego la igualdad se da si y sólo si esto es no nulo.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 \begin_inset Formula $A[X]$
 \end_inset
@@ -461,7 +471,8 @@ cuerpo de las funciones racionales
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Enumerate
 \begin_inset Argument item:1
@@ -523,6 +534,11 @@ Sean
  tampoco lo es.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Propiedad universal
 \end_layout
@@ -581,10 +597,10 @@ PUAP
 \end_inset
 
 
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $\tilde{f}$
 \end_inset
@@ -620,7 +636,11 @@ lo que prueba la unicidad.
 
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $A[X]$
 \end_inset
@@ -671,10 +691,10 @@ lo que prueba la unicidad.
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Tomando 
 \begin_inset Formula $v$
 \end_inset
@@ -740,7 +760,11 @@ Tomando
  es el isomorfismo buscado.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Así:
 \end_layout
@@ -808,17 +832,21 @@ función polinómica
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $S_{b}$
 \end_inset
 
  se obtiene al aplicar la PUAP a la inclusión.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Dado 
 \begin_inset Formula $a\in A$
@@ -837,10 +865,10 @@ Dado
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $S_{X-a}(S_{X+a}(X))=S_{X-a}(X+a)=X$
 \end_inset
 
@@ -872,7 +900,11 @@ Dado
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $A$
@@ -883,10 +915,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 El homomorfismo 
 \begin_inset Formula $A[X]\to A$
 \end_inset
@@ -898,7 +930,11 @@ El homomorfismo
 , y basta aplicar el primer teorema de isomorfía.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Todo homomorfismo de anillos 
 \begin_inset Formula $f:A\to B$
@@ -921,10 +957,10 @@ que es inyectivo o suprayectivo si lo es
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Se obtiene de aplicar la PUAP a la composición de la inclusión 
 \begin_inset Formula $B\to B[X]$
 \end_inset
@@ -936,7 +972,11 @@ Se obtiene de aplicar la PUAP a la composición de la inclusión
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $A$
@@ -955,14 +995,18 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Basta aplicar lo anterior al homomorfismo inyectivo inclusión.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $I$
@@ -1001,10 +1045,10 @@ Su núcleo es
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Se obtiene de aplicar la PUAP a la proyección 
 \begin_inset Formula $A\to A/I$
 \end_inset
@@ -1017,7 +1061,11 @@ Se obtiene de aplicar la PUAP a la proyección
  es un ideal, y entonces basta aplicar el primer teorema de isomorfía.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Raíces de polinomios
 \end_layout
@@ -1078,7 +1126,11 @@ noprefix "false"
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1205,6 +1257,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 \begin_inset Float algorithm
 wide false
@@ -1368,7 +1425,11 @@ Teorema del resto:
 \end_inset
 
 .
- En efecto, si 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, si 
 \begin_inset Formula $f=q(X-a)+r$
 \end_inset
 
@@ -1389,6 +1450,10 @@ Teorema del resto:
 \end_inset
 
 .
+\end_layout
+
+\end_inset
+
  De aquí se obtiene el 
 \series bold
 teorema de Ruffini
@@ -1528,7 +1593,11 @@ La multiplicidad de
 \end_inset
 
  no es raíz.
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1601,6 +1670,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Si 
 \begin_inset Formula $D$
@@ -1651,7 +1725,11 @@ Si
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -1725,6 +1803,11 @@ Demostración:
  
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
@@ -1767,10 +1850,10 @@ Para
 \end_inset
 
  son iguales.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sean 
 \begin_inset Formula $a_{1},\dots,a_{m}$
 \end_inset
@@ -1790,7 +1873,11 @@ Sean
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $D$
 \end_inset
@@ -1804,9 +1891,9 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1832,6 +1919,7 @@ Si hubiera
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1854,6 +1942,11 @@ Si
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Como ejemplo de lo anterior, por el teorema pequeño de Fermat, dado un primo
  
@@ -1913,10 +2006,10 @@ derivada
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula 
 \begin{multline*}
 D(aP+bQ)=D\left(a\sum_{k}p_{k}X^{k}+b\sum_{k}q_{k}X^{k}\right)=D\left(\sum_{k}(ap_{k}+bq_{k})X^{k}\right)=\\
@@ -1928,16 +2021,20 @@ D(aP+bQ)=D\left(a\sum_{k}p_{k}X^{k}+b\sum_{k}q_{k}X^{k}\right)=D\left(\sum_{k}(a
 
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $(PQ)'=P'Q+PQ'$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula 
 \begin{multline*}
 D(PQ)=D\left(\left(\sum_{k}p_{k}X^{k}\right)\left(\sum_{k}q_{k}X^{k}\right)\right)=D\left(\sum_{k}\left(\sum_{i=0}^{k}p_{i}q_{k-i}\right)X^{k}\right)=\\
@@ -1951,16 +2048,20 @@ D(PQ)=D\left(\left(\sum_{k}p_{k}X^{k}\right)\left(\sum_{k}q_{k}X^{k}\right)\righ
 
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $(P^{n})'=nP^{n-1}P'$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $P^{n-1}$
 \end_inset
 
@@ -1993,7 +2094,11 @@ D(PQ)=D\left(\left(\sum_{k}p_{k}X^{k}\right)\left(\sum_{k}q_{k}X^{k}\right)\righ
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Dados un dominio 
 \begin_inset Formula $D$
@@ -2024,7 +2129,11 @@ Dados un dominio
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -2137,6 +2246,11 @@ Demostración:
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Divisibilidad en anillos de polinomios
 \end_layout
@@ -2155,7 +2269,8 @@ Dado un anillo
 \end_inset
 
  es un cuerpo.
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $1\implies2]$
@@ -2270,6 +2385,11 @@ Dado un anillo
  son invertibles.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Sean 
 \begin_inset Formula $D$
@@ -3150,22 +3270,6 @@ status open
 \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
 Si 
 \begin_inset Formula $D$
 \end_inset
@@ -3208,7 +3312,12 @@ Si
 \end_inset
 
 .
- Esto está bien definido, pues si 
+ Esto está bien definido
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+, pues si 
 \begin_inset Formula $b_{1}\sim b_{2}$
 \end_inset
 
@@ -3220,28 +3329,17 @@ Si
 \begin_inset Formula $(ab_{2})D^{*}=(aub_{1})D^{*}=\{ab_{1}uv\}_{v\in D^{*}}=\{ab_{1}v\}_{v\in D^{*}}=(ab_{1})D^{*}$
 \end_inset
 
-.
- Además, 
-\begin_inset Formula $a(b(cD^{*}))=(ab)(cD^{*})$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
 
-\begin_layout Plain Layout
-
-
-\backslash
-end{samepage}
 \end_layout
 
 \end_inset
 
+.
+ Además, 
+\begin_inset Formula $a(b(cD^{*}))=(ab)(cD^{*})$
+\end_inset
 
+.
 \end_layout
 
 \begin_layout Standard
@@ -3274,7 +3372,12 @@ Definimos
 \end_inset
 
 .
- Esto está bien definido, pues si 
+ Esto está bien definido
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+, pues si 
 \begin_inset Formula $a_{1}p,a_{2}p\in D[X]$
 \end_inset
 
@@ -3286,6 +3389,11 @@ Definimos
 \begin_inset Formula $a_{1}^{-1}c(a_{1}p)=a_{2}^{-1}c(a_{2}p)$
 \end_inset
 
+
+\end_layout
+
+\end_inset
+
 .
  Si 
 \begin_inset Formula $c(p)=aD^{*}$
@@ -3344,10 +3452,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $a\mid p$
 \end_inset
 
@@ -3370,16 +3478,20 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $c(ap)=ac(p)$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $a\in D$
 \end_inset
@@ -3404,15 +3516,19 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $p\in D[X]\iff c(p)\in D$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3429,6 +3545,7 @@ status open
 Obvio.
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3572,6 +3689,11 @@ Sea
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Un polinomio 
 \begin_inset Formula $p$
@@ -3810,10 +3932,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sean 
 \begin_inset Formula $g,h\in K[X]$
 \end_inset
@@ -3833,7 +3955,11 @@ Sean
  es unidad.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $\text{gr}(f)>1$
@@ -3856,10 +3982,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sean 
 \begin_inset Formula $a$
 \end_inset
@@ -3887,7 +4013,11 @@ Sean
  son unidades.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $\text{gr}(f)\in\{2,3\}$
@@ -3906,9 +4036,9 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3925,6 +4055,7 @@ status open
 Es el contrarrecíproco de lo anterior.
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -3983,6 +4114,11 @@ De haber
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Si 
 \begin_inset Formula $D$
@@ -4021,7 +4157,11 @@ Si
 \end_inset
 
 .
- En efecto, sea 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, sea 
 \begin_inset Formula $t=\frac{r}{s}$
 \end_inset
 
@@ -4072,6 +4212,11 @@ Si
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
@@ -4126,7 +4271,11 @@ Criterio de reducción:
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -4202,6 +4351,11 @@ Demostración:
  
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 En particular, si 
 \begin_inset Formula $p\in\mathbb{Z}$
@@ -4276,7 +4430,11 @@ Criterio de Eisenstein:
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -4353,6 +4511,11 @@ Demostración:
  es análogo.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Así:
 \end_layout
@@ -4375,10 +4538,10 @@ Si
 \end_inset
 
  es irreducible.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $X^{n}-a$
 \end_inset
 
@@ -4393,7 +4556,11 @@ Si
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Para 
 \begin_inset Formula $n\geq3$
@@ -4474,10 +4641,10 @@ de 1
 \end_inset
 
  es irreducible.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Usando el automorfismo de sustitución en 
 \begin_inset Formula $X+1$
 \end_inset
@@ -4521,7 +4688,11 @@ Entonces
  y podemos aplicar el criterio de Eisenstein.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Polinomios en varias indeterminadas
 \end_layout
@@ -4581,7 +4752,17 @@ polinomios en
 \begin_inset Formula $n\in\mathbb{N}^{*}$
 \end_inset
 
-, por inducción:
+
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+, por inducción
+\end_layout
+
+\end_inset
+
+:
 \end_layout
 
 \begin_layout Enumerate
@@ -4691,7 +4872,11 @@ con
 \end_inset
 
 .
- 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+
 \series bold
 Demostración:
 \series default
@@ -4772,17 +4957,6 @@ p=\sum_{i\in\mathbb{N}^{n}}p_{i}X_{1}^{i_{1}}\cdots X_{n}^{i_{n}}=\sum_{i\in\mat
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-begin{samepage}
-\end_layout
-
 \end_inset
 
 
@@ -4897,22 +5071,6 @@ Dados un anillo conmutativo
 \end_layout
 
 \begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-end{samepage}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
 Así:
 \end_layout