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-rw-r--r--ac/n1.lyx48
-rw-r--r--ac/n2.lyx14
-rw-r--r--ac/n3.lyx8
3 files changed, 35 insertions, 35 deletions
diff --git a/ac/n1.lyx b/ac/n1.lyx
index 3cbfecf..c64daaf 100644
--- a/ac/n1.lyx
+++ b/ac/n1.lyx
@@ -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
diff --git a/ac/n2.lyx b/ac/n2.lyx
index d1f9070..07960c8 100644
--- a/ac/n2.lyx
+++ b/ac/n2.lyx
@@ -771,7 +771,7 @@ Para
\end_inset
, los
-\begin_inset Formula $I_{n}\coloneqq\{a:\forall k>n,a_{k}=0\}$
+\begin_inset Formula $I_{n}\coloneqq\{a\mid \forall k>n,a_{k}=0\}$
\end_inset
cumplen
@@ -779,7 +779,7 @@ Para
\end_inset
y los
-\begin_inset Formula $J_{n}\coloneqq\{a:\forall k<n,a_{k}=0\}$
+\begin_inset Formula $J_{n}\coloneqq\{a\mid \forall k<n,a_{k}=0\}$
\end_inset
cumplen
@@ -1333,7 +1333,7 @@ Dados
\end_inset
, llamamos
-\begin_inset Formula $(I:S)=\{a\in A:aS\subseteq I\}$
+\begin_inset Formula $(I:S)=\{a\in A\mid aS\subseteq I\}$
\end_inset
.
@@ -1491,7 +1491,7 @@ anulador
\end_inset
a
-\begin_inset Formula $\text{ann}_{A}(X)\coloneqq(0:X)=\{a\in A:aX=0\}$
+\begin_inset Formula $\text{ann}_{A}(X)\coloneqq(0:X)=\{a\in A\mid aX=0\}$
\end_inset
, y entonces
@@ -1719,7 +1719,7 @@ Claramente
\end_layout
\begin_layout Standard
-\begin_inset Formula $(P:(a))=\{c\in A:c(a)=(ca)\subseteq P\}=\{c\in A:ac\in P\}$
+\begin_inset Formula $(P:(a))=\{c\in A\mid c(a)=(ca)\subseteq P\}=\{c\in A\mid ac\in P\}$
\end_inset
, y entonces
@@ -2218,7 +2218,7 @@ dimensión de Krull
es
\begin_inset Formula
\[
-\dim A\coloneqq\text{Kdim}A\coloneqq\sup\{n\in\mathbb{N}:\exists P_{0},\dots,P_{n}\trianglelefteq_{\text{p}}A:P_{0}\subsetneq\dots\subsetneq P_{n}\}\in\mathbb{N}\cup\{\infty\},
+\dim A\coloneqq\text{Kdim}A\coloneqq\sup\{n\in\mathbb{N}\mid \exists P_{0},\dots,P_{n}\trianglelefteq_{\text{p}}A:P_{0}\subsetneq\dots\subsetneq P_{n}\}\in\mathbb{N}\cup\{\infty\},
\]
\end_inset
@@ -2443,7 +2443,7 @@ Dado
.
Si no lo fuera,
-\begin_inset Formula $\Omega\coloneqq\{K\trianglelefteq A:KI\neq0\}\neq\emptyset$
+\begin_inset Formula $\Omega\coloneqq\{K\trianglelefteq A\mid KI\neq0\}\neq\emptyset$
\end_inset
, pues
diff --git a/ac/n3.lyx b/ac/n3.lyx
index 0293687..845df67 100644
--- a/ac/n3.lyx
+++ b/ac/n3.lyx
@@ -304,7 +304,7 @@ anulador
\end_inset
a
-\begin_inset Formula $\text{ann}_{M}(X)\coloneqq\{m\in M:Xm=0\}\leq_{A}M$
+\begin_inset Formula $\text{ann}_{M}(X)\coloneqq\{m\in M\mid Xm=0\}\leq_{A}M$
\end_inset
.
@@ -339,7 +339,7 @@ externa
)
\begin_inset Formula
\[
-\bigoplus_{i\in I}M_{i}\coloneqq\left\{ x\in\prod_{i\in I}M_{i}:\{i\in I:x_{i}\neq0\}\text{ finito}\right\} .
+\bigoplus_{i\in I}M_{i}\coloneqq\left\{ x\in\prod_{i\in I}M_{i}\;\middle|\;\{i\in I\mid x_{i}\neq0\}\text{ finito}\right\} .
\]
\end_inset
@@ -645,7 +645,7 @@ Si
\end_inset
,
-\begin_inset Formula $\{f\in A[X]:\text{gr}f\leq n\}$
+\begin_inset Formula $\{f\in A[X]\mid\text{gr}f\leq n\}$
\end_inset
es un submódulo de
@@ -1296,7 +1296,7 @@ Si
\end_inset
,
-\begin_inset Formula $_{A/I}\text{Mod}\equiv\{M\in_{A}\text{Mod}:IM=0\}$
+\begin_inset Formula $_{A/I}\text{Mod}\equiv\{M\in_{A}\text{Mod}\mid IM=0\}$
\end_inset
por la biyección
generated by cgit v1.2.3 (git 2.46.0) at 2025-10-27 02:40:48 +0000