Oops

1 files changed, 40 insertions, 40 deletions

diff --git a/ac/n1.lyx b/ac/n1.lyx
index c64daaf..41bc9ce 100644
--- a/ac/n1.lyx
+++ b/ac/n1.lyx
@@ -519,7 +519,7 @@ status open
 \end_inset
 
 , definimos 
-\begin_inset Formula $0_{\mathbb{Z}}a:=0$
+\begin_inset Formula $0_{\mathbb{Z}}a\coloneqq 0$
 \end_inset
 
 , y para 
@@ -527,16 +527,16 @@ status open
 \end_inset
 
 , 
-\begin_inset Formula $na:=(n-1)a+a$
+\begin_inset Formula $na\coloneqq (n-1)a+a$
 \end_inset
 
  y 
-\begin_inset Formula $(-n)a:=-(na)$
+\begin_inset Formula $(-n)a\coloneqq -(na)$
 \end_inset
 
 .
  Definimos 
-\begin_inset Formula $a^{0_{\mathbb{Z}}}:=1_{A}$
+\begin_inset Formula $a^{0_{\mathbb{Z}}}\coloneqq 1_{A}$
 \end_inset
 
 , para 
@@ -544,7 +544,7 @@ status open
 \end_inset
 
 , 
-\begin_inset Formula $a^{n}:=a^{n-1}a$
+\begin_inset Formula $a^{n}\coloneqq a^{n-1}a$
 \end_inset
 
 , y si 
@@ -552,7 +552,7 @@ status open
 \end_inset
 
  es invertible, 
-\begin_inset Formula $a^{-n}:=(a^{-1})^{n}$
+\begin_inset Formula $a^{-n}\coloneqq (a^{-1})^{n}$
 \end_inset
 
 .
@@ -1068,7 +1068,7 @@ Dado un anillo
 \end_inset
 
  dada por 
-\begin_inset Formula $\mu(n):=n1$
+\begin_inset Formula $\mu(n)\coloneqq n1$
 \end_inset
 
  es el único homomorfismo de anillos de 
@@ -1100,7 +1100,7 @@ proyección
 \end_inset
 
  dada por 
-\begin_inset Formula $p_{j}(a):=a_{j}$
+\begin_inset Formula $p_{j}(a)\coloneqq a_{j}$
 \end_inset
 
  es un homomorfismo.
@@ -1112,7 +1112,7 @@ La
 conjugación
 \series default
  de complejos, dada por 
-\begin_inset Formula $\overline{a+bi}:=a-bi$
+\begin_inset Formula $\overline{a+bi}\coloneqq a-bi$
 \end_inset
 
  para 
@@ -2529,7 +2529,7 @@ equivalentes
 \end_inset
 
  de 
-\begin_inset Formula $\mathbb{N}_{n}:=\{1,\dots,n\}$
+\begin_inset Formula $\mathbb{N}_{n}\coloneqq \{1,\dots,n\}$
 \end_inset
 
  tal que para 
@@ -3320,7 +3320,7 @@ subanillo primo
 \end_inset
 
  a 
-\begin_inset Formula $\mathbb{Z}1:=\{n1_{A}\}_{n\in\mathbb{Z}}$
+\begin_inset Formula $\mathbb{Z}1\coloneqq \{n1_{A}\}_{n\in\mathbb{Z}}$
 \end_inset
 
 , el menor subanillo de 
@@ -4321,7 +4321,7 @@ Dado
 \end_inset
 
 , llamamos 
-\begin_inset Formula $\mathbb{Z}_{n}:=\frac{\mathbb{Z}}{n\mathbb{Z}}=\{0+n\mathbb{Z},\dots,(n-1)+n\mathbb{Z}\}$
+\begin_inset Formula $\mathbb{Z}_{n}\coloneqq \frac{\mathbb{Z}}{n\mathbb{Z}}=\{0+n\mathbb{Z},\dots,(n-1)+n\mathbb{Z}\}$
 \end_inset
 
 .
@@ -8914,7 +8914,7 @@ Sean
 \end_inset
 
  un dominio y 
-\begin_inset Formula $X:=D\times(D\setminus\{0\})$
+\begin_inset Formula $X\coloneqq D\times(D\setminus\{0\})$
 \end_inset
 
 , definimos la relación binaria 
@@ -8927,7 +8927,7 @@ Sean
 
  Esta relación es de equivalencia.
  Llamamos 
-\begin_inset Formula $a/s:=\frac{a}{s}:=[(a,s)]\in Q(D):=X/\sim$
+\begin_inset Formula $a/s\coloneqq \frac{a}{s}\coloneqq [(a,s)]\in Q(D)\coloneqq X/\sim$
 \end_inset
 
 , y las operaciones
@@ -9030,7 +9030,7 @@ de cocientes
 \end_inset
 
  dada por 
-\begin_inset Formula $u(a):=a/1$
+\begin_inset Formula $u(a)\coloneqq a/1$
 \end_inset
 
  es un homomorfismo inyectivo, por lo que podemos ver a 
@@ -9082,7 +9082,7 @@ Propiedad universal del cuerpo de fracciones:
 \end_inset
 
  dada por 
-\begin_inset Formula $u(a):=a/1$
+\begin_inset Formula $u(a)\coloneqq a/1$
 \end_inset
 
 :
@@ -9342,7 +9342,7 @@ polinomios constantes
 \end_inset
 
  e 
-\begin_inset Formula $I[X]:=\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0},\dots,a_{n}\in I\}$
+\begin_inset Formula $I[X]\coloneqq \{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0},\dots,a_{n}\in I\}$
 \end_inset
 
  son ideales de 
@@ -9354,7 +9354,7 @@ polinomios constantes
 
 \begin_layout Standard
 Dado 
-\begin_inset Formula $p:=\sum_{k\in\mathbb{N}}p_{k}X^{k}\in A[X]\setminus\{0\}$
+\begin_inset Formula $p\coloneqq \sum_{k\in\mathbb{N}}p_{k}X^{k}\in A[X]\setminus\{0\}$
 \end_inset
 
 , llamamos 
@@ -9366,7 +9366,7 @@ grado
 \end_inset
 
  a 
-\begin_inset Formula $\text{gr}(p):=\max\{k\in\mathbb{N}\mid p_{k}\neq0\}$
+\begin_inset Formula $\text{gr}(p)\coloneqq \max\{k\in\mathbb{N}\mid p_{k}\neq0\}$
 \end_inset
 
 , 
@@ -9677,7 +9677,7 @@ función polinómica
 \end_inset
 
  dada por 
-\begin_inset Formula $\hat{p}(b):=S_{b}(p)$
+\begin_inset Formula $\hat{p}(b)\coloneqq S_{b}(p)$
 \end_inset
 
 .
@@ -9916,7 +9916,7 @@ Para
 \end_inset
 
 , existe 
-\begin_inset Formula $m:=\max\{k\in\mathbb{N}\mid(X-a)^{k}\mid f\}$
+\begin_inset Formula $m\coloneqq \max\{k\in\mathbb{N}\mid(X-a)^{k}\mid f\}$
 \end_inset
 
 .
@@ -10142,19 +10142,19 @@ Dado un anillo conmutativo
 derivada
 \series default
  de 
-\begin_inset Formula $P:=\sum_{k}a_{k}X^{k}\in A[X]$
+\begin_inset Formula $P\coloneqq \sum_{k}a_{k}X^{k}\in A[X]$
 \end_inset
 
  como 
-\begin_inset Formula $P':=D(P):=\sum_{k\geq1}ka_{k}X^{k-1}$
+\begin_inset Formula $P'\coloneqq D(P)\coloneqq \sum_{k\geq1}ka_{k}X^{k-1}$
 \end_inset
 
 , y escribimos 
-\begin_inset Formula $P^{(0)}:=P$
+\begin_inset Formula $P^{(0)}\coloneqq P$
 \end_inset
 
  y 
-\begin_inset Formula $P^{(n+1)}:=P^{(n)\prime}$
+\begin_inset Formula $P^{(n+1)}\coloneqq P^{(n)\prime}$
 \end_inset
 
 .
@@ -10444,11 +10444,11 @@ Definimos
 \end_inset
 
  tal que, para 
-\begin_inset Formula $p:=\sum_{k\geq0}p_{k}X^{k}\in D[X]$
+\begin_inset Formula $p\coloneqq \sum_{k\geq0}p_{k}X^{k}\in D[X]$
 \end_inset
 
 , 
-\begin_inset Formula $c(p):=\{x\mid x=\text{mcd}_{k\geq0}p_{k}\}$
+\begin_inset Formula $c(p)\coloneqq \{x\mid x=\text{mcd}_{k\geq0}p_{k}\}$
 \end_inset
 
 , y para 
@@ -10464,7 +10464,7 @@ Definimos
 \end_inset
 
 , 
-\begin_inset Formula $c(p):=a^{-1}c(ap)$
+\begin_inset Formula $c(p)\coloneqq a^{-1}c(ap)$
 \end_inset
 
 .
@@ -10738,11 +10738,11 @@ Si
 \end_inset
 
 , 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in D[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in D[X]$
 \end_inset
 
  y 
-\begin_inset Formula $n:=\text{gr}(f)$
+\begin_inset Formula $n\coloneqq \text{gr}(f)$
 \end_inset
 
 , todas las raíces de 
@@ -10830,11 +10830,11 @@ En particular, si
 \end_inset
 
  es primo, 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in\mathbb{Z}[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in\mathbb{Z}[X]$
 \end_inset
 
  es primitivo, 
-\begin_inset Formula $n:=\text{gr}(f)$
+\begin_inset Formula $n\coloneqq \text{gr}(f)$
 \end_inset
 
 , 
@@ -10870,11 +10870,11 @@ Criterio de Eisenstein:
 \end_inset
 
  un DFU, 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in D[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in D[X]$
 \end_inset
 
  primitivo y 
-\begin_inset Formula $n:=\text{gr}f$
+\begin_inset Formula $n\coloneqq \text{gr}f$
 \end_inset
 
 , si existe un irreducible 
@@ -10967,7 +10967,7 @@ de 1
 \end_inset
 
 , donde 
-\begin_inset Formula $\Phi_{n}(X):=X^{n-1}+X^{n-2}+\dots+X+1$
+\begin_inset Formula $\Phi_{n}(X)\coloneqq X^{n-1}+X^{n-2}+\dots+X+1$
 \end_inset
 
  es el 
@@ -11028,7 +11028,7 @@ anillo de polinomios
 \end_inset
 
  como 
-\begin_inset Formula $A[X_{1},\dots,X_{n}]:=A[X_{1},\dots,X_{n-1}][X_{n}]$
+\begin_inset Formula $A[X_{1},\dots,X_{n}]\coloneqq A[X_{1},\dots,X_{n-1}][X_{n}]$
 \end_inset
 
 .
@@ -11126,7 +11126,7 @@ Dados
 \end_inset
 
  e 
-\begin_inset Formula $i:=(i_{1},\dots,i_{n})\in\mathbb{N}^{n}$
+\begin_inset Formula $i\coloneqq (i_{1},\dots,i_{n})\in\mathbb{N}^{n}$
 \end_inset
 
 , llamamos a 
@@ -11303,7 +11303,7 @@ homomorfismo de sustitución
 \end_inset
 
  viene dado por 
-\begin_inset Formula $p(b_{1},\dots,b_{n}):=S(p):=\sum_{i\in\mathbb{N}^{n}}p_{i}b_{1}^{i_{1}}\cdots b_{n}^{i_{n}}$
+\begin_inset Formula $p(b_{1},\dots,b_{n})\coloneqq S(p)\coloneqq \sum_{i\in\mathbb{N}^{n}}p_{i}b_{1}^{i_{1}}\cdots b_{n}^{i_{n}}$
 \end_inset
 
 .
@@ -11356,7 +11356,7 @@ Sean
 \end_inset
 
  con inversa 
-\begin_inset Formula $\tau:=\sigma^{-1}$
+\begin_inset Formula $\tau\coloneqq \sigma^{-1}$
 \end_inset
 
 , tomando 
@@ -11399,7 +11399,7 @@ Todo homomorfismo de anillos conmutativos
 \end_inset
 
  dado por 
-\begin_inset Formula $\hat{f}(p):=\sum_{i\in\mathbb{N}^{n}}f(p_{i})X_{1}^{i_{1}}\cdots X_{n}^{i_{n}}$
+\begin_inset Formula $\hat{f}(p)\coloneqq \sum_{i\in\mathbb{N}^{n}}f(p_{i})X_{1}^{i_{1}}\cdots X_{n}^{i_{n}}$
 \end_inset
 
 .