diff options
Diffstat (limited to 'ealg')
| -rw-r--r-- | ealg/n1.lyx | 12 | ||||
| -rw-r--r-- | ealg/n2.lyx | 2 | ||||
| -rw-r--r-- | ealg/n4.lyx | 8 | ||||
| -rw-r--r-- | ealg/n5.lyx | 2 | ||||
| -rw-r--r-- | ealg/n6.lyx | 6 | ||||
| -rw-r--r-- | ealg/n7.lyx | 8 |
6 files changed, 19 insertions, 19 deletions
diff --git a/ealg/n1.lyx b/ealg/n1.lyx index 7068e05..a5d022d 100644 --- a/ealg/n1.lyx +++ b/ealg/n1.lyx @@ -223,7 +223,7 @@ 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 , @@ -831,7 +831,7 @@ 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 . @@ -968,7 +968,7 @@ 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 . @@ -1875,7 +1875,7 @@ teorema \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 [...] si @@ -3967,11 +3967,11 @@ Queremos ver que, para . Con esto, sean -\begin_inset Formula $A:=\{i\in\mathbb{N}^{n}:a_{i}\neq0\}$ +\begin_inset Formula $A:=\{i\in\mathbb{N}^{n}\mid a_{i}\neq0\}$ \end_inset , -\begin_inset Formula $B:=\{j\in\mathbb{N}^{n}:b_{j}\neq0\}$ +\begin_inset Formula $B:=\{j\in\mathbb{N}^{n}\mid b_{j}\neq0\}$ \end_inset , diff --git a/ealg/n2.lyx b/ealg/n2.lyx index a006108..cbcd97d 100644 --- a/ealg/n2.lyx +++ b/ealg/n2.lyx @@ -4611,7 +4611,7 @@ clausura algebraica es \begin_inset Formula \[ -\overline{K}_{L}:=\{\alpha\in L:\alpha\text{ es algebraico sobre }K\}. +\overline{K}_{L}:=\{\alpha\in L\mid \alpha\text{ es algebraico sobre }K\}. \] \end_inset diff --git a/ealg/n4.lyx b/ealg/n4.lyx index e9f8c50..4a46a08 100644 --- a/ealg/n4.lyx +++ b/ealg/n4.lyx @@ -1089,7 +1089,7 @@ grupo de Galois \end_inset lleva raíces a raíces y por tanto -\begin_inset Formula $\sigma|_{\{\alpha_{1},\dots,\alpha_{n}\}}:\{\alpha_{1},\dots,\alpha_{n}\}\to\{\alpha_{1},\dots,\alpha_{n}\}$ +\begin_inset Formula $\sigma|_{\{\alpha_{1},\dots,\alpha_{n}\}}\mid \{\alpha_{1},\dots,\alpha_{n}\}\to\{\alpha_{1},\dots,\alpha_{n}\}$ \end_inset es inyectiva por serlo @@ -1491,7 +1491,7 @@ teorema \end_inset , -\begin_inset Formula $K(\{\alpha\in\overline{K}:\exists f\in{\cal P}:f(\alpha)=0\})$ +\begin_inset Formula $K(\{\alpha\in\overline{K}\mid \exists f\in{\cal P}:f(\alpha)=0\})$ \end_inset , por lo que existe un cuerpo de descomposición de @@ -2010,7 +2010,7 @@ Para cada \end_inset elementos y viene dado por -\begin_inset Formula $\mathbb{F}_{p^{n}}:=\{\alpha\in\overline{\mathbb{Z}_{p}}:\alpha^{p^{n}}=\alpha\}$ +\begin_inset Formula $\mathbb{F}_{p^{n}}:=\{\alpha\in\overline{\mathbb{Z}_{p}}\mid \alpha^{p^{n}}=\alpha\}$ \end_inset . @@ -2019,7 +2019,7 @@ Para cada \begin_deeper \begin_layout Standard Sea -\begin_inset Formula $S:=\{\alpha\in\overline{\mathbb{Z}_{p}}:\alpha^{p^{n}}=\alpha\}$ +\begin_inset Formula $S:=\{\alpha\in\overline{\mathbb{Z}_{p}}\mid \alpha^{p^{n}}=\alpha\}$ \end_inset el conjunto de raíces de diff --git a/ealg/n5.lyx b/ealg/n5.lyx index a3eaed8..18c97fd 100644 --- a/ealg/n5.lyx +++ b/ealg/n5.lyx @@ -112,7 +112,7 @@ de uno , y llamamos \begin_inset Formula \[ -{\cal U}_{n}(K):=\{\xi\in K:\xi^{n}=1\}=\{\xi\in K:o_{K^{*}}(\xi)\mid n\}. +{\cal U}_{n}(K):=\{\xi\in K\mid \xi^{n}=1\}=\{\xi\in K\mid o_{K^{*}}(\xi)\mid n\}. \] \end_inset diff --git a/ealg/n6.lyx b/ealg/n6.lyx index 343a1ac..fd441a7 100644 --- a/ealg/n6.lyx +++ b/ealg/n6.lyx @@ -243,7 +243,7 @@ Demostración: \end_inset y -\begin_inset Formula $R:=\{\alpha_{1}:=\alpha,\dots,\alpha_{m}\}$ +\begin_inset Formula $R:=\{\alpha_{1}\mid =\alpha,\dots,\alpha_{m}\}$ \end_inset el conjunto de las raíces de @@ -354,7 +354,7 @@ teorema \end_inset Sean -\begin_inset Formula ${\cal P}:=\{f_{\alpha}:=\text{Irr}(\alpha,K)\}_{\alpha\in L}\subseteq K[X]\setminus0$ +\begin_inset Formula ${\cal P}:=\{f_{\alpha}\mid =\text{Irr}(\alpha,K)\}_{\alpha\in L}\subseteq K[X]\setminus0$ \end_inset y @@ -1107,7 +1107,7 @@ clausura normal , y viene dada por \begin_inset Formula \[ -N:=\bigcap\{E\text{ intermedio en }L\subseteq\overline{L}:K\subseteq E\text{ normal}\}. +N:=\bigcap\{E\text{ intermedio en }L\subseteq\overline{L}\mid K\subseteq E\text{ normal}\}. \] \end_inset diff --git a/ealg/n7.lyx b/ealg/n7.lyx index 2faa1a1..f5f15b6 100644 --- a/ealg/n7.lyx +++ b/ealg/n7.lyx @@ -83,7 +83,7 @@ \begin_layout Standard \begin_inset Formula \[ -\text{Gal}(K(X)/K)=\bigg\{\sigma\,\Big\vert\,\exists a,b,c,d\in K:\bigg(ad-bc\neq0\land\sigma(X)=\frac{aX+b}{cX+d}\bigg)\bigg\}. +\text{Gal}(K(X)/K)=\bigg\{\sigma\,\Big\vert\,\exists a,b,c,d\in K\mid \bigg(ad-bc\neq0\land\sigma(X)=\frac{aX+b}{cX+d}\bigg)\bigg\}. \] \end_inset @@ -139,8 +139,8 @@ conexión de Galois dado por \begin_inset Formula \begin{align*} -f(F):=F' & :=\{\sigma\in G:\forall\alpha\in F,\sigma(\alpha)=\alpha\}=\text{Gal}(L/F),\\ -g(H):=H' & :=\{\alpha\in L:\forall\sigma\in H,\sigma(\alpha)=\alpha\}=\bigcap_{\sigma\in H}\text{Fix}\sigma. +f(F):=F' & :=\{\sigma\in G\mid \forall\alpha\in F,\sigma(\alpha)=\alpha\}=\text{Gal}(L/F),\\ +g(H):=H' & :=\{\alpha\in L\mid \forall\sigma\in H,\sigma(\alpha)=\alpha\}=\bigcap_{\sigma\in H}\text{Fix}\sigma. \end{align*} \end_inset @@ -150,7 +150,7 @@ En particular, para \end_inset , -\begin_inset Formula $K(\beta)'=\{\sigma\in G:\sigma(\beta)=\beta\}$ +\begin_inset Formula $K(\beta)'=\{\sigma\in G\mid \sigma(\beta)=\beta\}$ \end_inset , y para |