diff options
Diffstat (limited to 'ac/n1.lyx')
| -rw-r--r-- | ac/n1.lyx | 48 |
1 files changed, 24 insertions, 24 deletions
@@ -799,7 +799,7 @@ status open \backslash -begin{reminder}{ga} +begin{reminder}{GyA} \end_layout \end_inset @@ -3379,7 +3379,7 @@ Dado un espacio topológico \end_inset , -\begin_inset Formula $\{f\in\mathbb{R}^{X}:f\text{ continua}\}$ +\begin_inset Formula $\{f\in\mathbb{R}^{X}\mid f\text{ continua}\}$ \end_inset es un subanillo de @@ -3404,7 +3404,7 @@ Dado un espacio vectorial \end_inset , -\begin_inset Formula $\{f\in V^{V}:f\text{ lineal}\}$ +\begin_inset Formula $\{f\in V^{V}\mid f\text{ lineal}\}$ \end_inset es un subanillo de @@ -3433,7 +3433,7 @@ Dado un anillo \end_inset , -\begin_inset Formula $\{f\in A^{X}:f\text{ constante}\}$ +\begin_inset Formula $\{f\in A^{X}\mid f\text{ constante}\}$ \end_inset es un subanillo de @@ -3893,7 +3893,7 @@ ideal de a \begin_inset Formula \[ -(S)\coloneqq\bigcap\{I\trianglelefteq A:S\subseteq I\}=\{a_{1}s_{1}+\dots+a_{n}s_{n}\}_{n\in\mathbb{N},a\in A^{n},s\in S^{n}}, +(S)\coloneqq\bigcap\{I\trianglelefteq A\mid S\subseteq I\}=\{a_{1}s_{1}+\dots+a_{n}s_{n}\}_{n\in\mathbb{N},a\in A^{n},s\in S^{n}}, \] \end_inset @@ -3912,7 +3912,7 @@ conjunto generador . En efecto, -\begin_inset Formula $\bigcap\{I\trianglelefteq A:S\subseteq I\}$ +\begin_inset Formula $\bigcap\{I\trianglelefteq A\mid S\subseteq I\}$ \end_inset es un ideal de @@ -5609,7 +5609,7 @@ Dado un homomorfismo de anillos , la extensión es una biyección \begin_inset Formula \[ -\{I\trianglelefteq A:\ker f\subseteq I\}\to\{J\trianglelefteq\text{Im}f\}, +\{I\trianglelefteq A\mid\ker f\subseteq I\}\to\{J\trianglelefteq\text{Im}f\}, \] \end_inset @@ -5715,7 +5715,7 @@ Si es la proyección canónica, \begin_inset Formula \[ -\rho:\{J\trianglelefteq A:I\subseteq J\}\to\{K\trianglelefteq A/I\} +\rho:\{J\trianglelefteq A\mid I\subseteq J\}\to\{K\trianglelefteq A/I\} \] \end_inset @@ -5821,7 +5821,7 @@ Hay tantos ideales de \end_inset y -\begin_inset Formula $\{I\trianglelefteq\mathbb{Z}:(n)\subseteq I\}$ +\begin_inset Formula $\{I\trianglelefteq\mathbb{Z}\mid(n)\subseteq I\}$ \end_inset , pero @@ -6810,11 +6810,11 @@ espectro maximal \end_inset , la biyección -\begin_inset Formula $\{J\in{\cal L}(A):I\subseteq J\}\to{\cal L}(A/I)$ +\begin_inset Formula $\{J\in{\cal L}(A)\mid I\subseteq J\}\to{\cal L}(A/I)$ \end_inset del teorema de la correspondencia se restringe a una biyección -\begin_inset Formula $\{J\in\text{MaxSpec}(A):I\subseteq J\}\to\text{MaxSpec}(A/I)$ +\begin_inset Formula $\{J\in\text{MaxSpec}(A)\mid I\subseteq J\}\to\text{MaxSpec}(A/I)$ \end_inset . @@ -6911,7 +6911,7 @@ Si Demostración: \series default Sea -\begin_inset Formula $\Omega\coloneqq\{J\triangleleft A:I\subseteq J\}$ +\begin_inset Formula $\Omega\coloneqq\{J\triangleleft A\mid I\subseteq J\}$ \end_inset , @@ -7037,7 +7037,7 @@ radical de Jacobson \end_inset a -\begin_inset Formula $\text{Jac}(A)\coloneqq\bigcap\text{MaxSpec}(A)=\{a\in A:1+(a)\subseteq A^{*}\}$ +\begin_inset Formula $\text{Jac}(A)\coloneqq\bigcap\text{MaxSpec}(A)=\{a\in A\mid1+(a)\subseteq A^{*}\}$ \end_inset . @@ -7543,11 +7543,11 @@ espectro primo \end_inset , la biyección -\begin_inset Formula $\{J\in{\cal L}(A):I\subseteq J\}\to{\cal L}(A/I)$ +\begin_inset Formula $\{J\in{\cal L}(A)\mid I\subseteq J\}\to{\cal L}(A/I)$ \end_inset se restringe a una biyección -\begin_inset Formula $\{J\in\text{Spec}(A):I\subseteq J\}\to\text{Spec}(A/I)$ +\begin_inset Formula $\{J\in\text{Spec}(A)\mid I\subseteq J\}\to\text{Spec}(A/I)$ \end_inset . @@ -7992,7 +7992,7 @@ primo minimal sobre Demostración: \series default Sea -\begin_inset Formula $\Omega\coloneqq\{P\trianglelefteq_{\text{p}}A:I\subseteq P\subseteq Q\}$ +\begin_inset Formula $\Omega\coloneqq\{P\trianglelefteq_{\text{p}}A\mid I\subseteq P\subseteq Q\}$ \end_inset , @@ -8363,7 +8363,7 @@ Lema de Krull: \end_layout \begin_layout Enumerate -\begin_inset Formula ${\cal L}_{I,S}\coloneqq\{J\trianglelefteq A:I\subseteq J,J\cap S=\emptyset\}$ +\begin_inset Formula ${\cal L}_{I,S}\coloneqq\{J\trianglelefteq A\mid I\subseteq J,J\cap S=\emptyset\}$ \end_inset es un conjunto inductivo no vacío. @@ -8490,7 +8490,7 @@ radical a \begin_inset Formula \[ -\sqrt{I}\coloneqq\{x\in A:\exists n\in\mathbb{N}:x^{n}\in I\}=\bigcap\{J\trianglelefteq_{\text{r}}A:I\subseteq J\}=\bigcap\{J\trianglelefteq_{\text{p}}A:I\subseteq J\}, +\sqrt{I}\coloneqq\{x\in A\mid\exists n\in\mathbb{N}\mid x^{n}\in I\}=\bigcap\{J\trianglelefteq_{\text{r}}A\mid I\subseteq J\}=\bigcap\{J\trianglelefteq_{\text{p}}A\mid I\subseteq J\}, \] \end_inset @@ -8785,7 +8785,7 @@ euclídea \end_layout \begin_layout Enumerate -\begin_inset Formula $\forall a\in D,b\in D\setminus\{0\},\exists q,r\in D:(a=bq+r\land(r=0\lor\delta(r)<\delta(b)))$ +\begin_inset Formula $\forall a\in D,b\in D\setminus\{0\},\exists q,r\in D\mid(a=bq+r\land(r=0\lor\delta(r)<\delta(b)))$ \end_inset . @@ -9338,11 +9338,11 @@ polinomios constantes \end_inset , -\begin_inset Formula $\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]:a_{0}\in I\}$ +\begin_inset Formula $\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0}\in I\}$ \end_inset e -\begin_inset Formula $I[X]:=\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]:a_{0},\dots,a_{n}\in I\}$ +\begin_inset Formula $I[X]:=\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0},\dots,a_{n}\in I\}$ \end_inset son ideales de @@ -9366,7 +9366,7 @@ grado \end_inset a -\begin_inset Formula $\text{gr}(p):=\max\{k\in\mathbb{N}:p_{k}\neq0\}$ +\begin_inset Formula $\text{gr}(p):=\max\{k\in\mathbb{N}\mid p_{k}\neq0\}$ \end_inset , @@ -9916,7 +9916,7 @@ Para \end_inset , existe -\begin_inset Formula $m:=\max\{k\in\mathbb{N}:(X-a)^{k}\mid f\}$ +\begin_inset Formula $m:=\max\{k\in\mathbb{N}\mid(X-a)^{k}\mid f\}$ \end_inset . @@ -10448,7 +10448,7 @@ Definimos \end_inset , -\begin_inset Formula $c(p):=\{x:x=\text{mcd}_{k\geq0}p_{k}\}$ +\begin_inset Formula $c(p):=\{x\mid x=\text{mcd}_{k\geq0}p_{k}\}$ \end_inset , y para |