diff options
Diffstat (limited to 'ga/n5.lyx')
| -rw-r--r-- | ga/n5.lyx | 30 |
1 files changed, 15 insertions, 15 deletions
@@ -98,7 +98,7 @@ suma \end_inset a -\begin_inset Formula $\sum_{i\in I}B_{i}:=\{\sum_{i\in I}b_{i}\mid b_{i}\in B_{i},\{i\in I\mid b_{i}\neq0\}\text{ es finito}\}$ +\begin_inset Formula $\sum_{i\in I}B_{i}\coloneqq \{\sum_{i\in I}b_{i}\mid b_{i}\in B_{i},\{i\in I\mid b_{i}\neq0\}\text{ es finito}\}$ \end_inset . @@ -404,7 +404,7 @@ Sean \begin_layout Standard Si -\begin_inset Formula $\hat{B}_{i}:=0\times\dots\times0\times B_{i}\times0\times\dots\times0\leq B_{1}\times\dots\times B_{n}$ +\begin_inset Formula $\hat{B}_{i}\coloneqq 0\times\dots\times0\times B_{i}\times0\times\dots\times0\leq B_{1}\times\dots\times B_{n}$ \end_inset , entonces @@ -420,7 +420,7 @@ Si \end_inset dada por -\begin_inset Formula $f(b_{1},\dots,b_{n}):=b_{1}+\dots+b_{n}$ +\begin_inset Formula $f(b_{1},\dots,b_{n})\coloneqq b_{1}+\dots+b_{n}$ \end_inset es un isomorfismo de grupos. @@ -704,7 +704,7 @@ subgrupo de es \begin_inset Formula \[ -t_{p}(A):=\{a\in A\mid \exists n\in\mathbb{N}\mid p^{n}a=0\}=\{a\in A\mid |a|\text{ es potencia de }p\}. +t_{p}(A):=\{a\in A\mid \exists n\in\mathbb{N}:p^{n}a=0\}=\{a\in A\mid|a|\text{ es potencia de }p\}. \] \end_inset @@ -799,7 +799,7 @@ Demostración: \end_inset , -\begin_inset Formula $q_{i}:=\prod_{j\neq i}p_{j}^{\alpha_{j}}$ +\begin_inset Formula $q_{i}\coloneqq \prod_{j\neq i}p_{j}^{\alpha_{j}}$ \end_inset , es claro que ningún primo divide a todos los @@ -860,7 +860,7 @@ Demostración: . Sea entonces -\begin_inset Formula $t_{i}:=\prod_{j\neq i}p_{j}^{\beta_{j}}$ +\begin_inset Formula $t_{i}\coloneqq \prod_{j\neq i}p_{j}^{\beta_{j}}$ \end_inset para cada @@ -931,7 +931,7 @@ Demostración: \begin_layout Standard Si -\begin_inset Formula $n:=p_{1}^{\alpha_{1}}\cdots p_{k}^{\alpha_{k}}$ +\begin_inset Formula $n\coloneqq p_{1}^{\alpha_{1}}\cdots p_{k}^{\alpha_{k}}$ \end_inset es una factorización prima @@ -1108,11 +1108,11 @@ Queda ver que . Sean -\begin_inset Formula $B:=\langle a\rangle$ +\begin_inset Formula $B\coloneqq \langle a\rangle$ \end_inset y -\begin_inset Formula $C:=A/B$ +\begin_inset Formula $C\coloneqq A/B$ \end_inset , si @@ -1171,7 +1171,7 @@ Dado \end_inset , tomamos -\begin_inset Formula $y:=x$ +\begin_inset Formula $y\coloneqq x$ \end_inset . @@ -1223,7 +1223,7 @@ Dado . Sea ahora -\begin_inset Formula $y:=x-rp^{m+t-s}a$ +\begin_inset Formula $y\coloneqq x-rp^{m+t-s}a$ \end_inset , entonces @@ -1723,11 +1723,11 @@ A=\langle a_{11}\rangle_{p_{1}^{\alpha_{1}}}\oplus\dots\oplus\langle a_{1m}\rang \end_inset , sean -\begin_inset Formula $b_{j}:=a_{1j}+\dots+a_{kj}$ +\begin_inset Formula $b_{j}\coloneqq a_{1j}+\dots+a_{kj}$ \end_inset y -\begin_inset Formula $d_{j}:=p_{1}^{\alpha_{1j}}\cdots p_{k}^{\alpha_{kj}}$ +\begin_inset Formula $d_{j}\coloneqq p_{1}^{\alpha_{1j}}\cdots p_{k}^{\alpha_{kj}}$ \end_inset , por el teorema chino de los restos, @@ -1809,7 +1809,7 @@ Todas las descomposiciones primarias de \begin_deeper \begin_layout Standard Sea -\begin_inset Formula $A:=A_{11}\oplus\dots\oplus A_{1m_{1}}\oplus\dots\oplus A_{k1}\oplus\dots\oplus A_{km_{k}}$ +\begin_inset Formula $A\coloneqq A_{11}\oplus\dots\oplus A_{1m_{1}}\oplus\dots\oplus A_{k1}\oplus\dots\oplus A_{km_{k}}$ \end_inset con @@ -1943,7 +1943,7 @@ Sea . Entonces, si -\begin_inset Formula $q:=p^{\alpha_{i}}$ +\begin_inset Formula $q\coloneqq p^{\alpha_{i}}$ \end_inset , |