diff options
Diffstat (limited to 'ac')
| -rw-r--r-- | ac/n1.lyx | 80 |
1 files changed, 40 insertions, 40 deletions
@@ -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 . |