diff options
Diffstat (limited to 'ga/n4.lyx')
| -rw-r--r-- | ga/n4.lyx | 66 |
1 files changed, 33 insertions, 33 deletions
@@ -2557,39 +2557,7 @@ status open \end_inset - -\begin_inset Formula $G\cong(\mathbb{Z}_{n},+)$ -\end_inset - - y -\begin_inset Formula $H\cong(\mathbb{Z}_{m},+)$ -\end_inset - -, y por el teorema chino de los restos para anillos, -\begin_inset Formula $\mathbb{Z}_{n}\times\mathbb{Z}_{m}\cong\frac{\mathbb{Z}}{nm\mathbb{Z}}=\mathbb{Z}_{nm}$ -\end_inset - - como anillos, luego los grupos aditivos también son isomorfos y -\begin_inset Formula $G\times H\cong(\mathbb{Z}_{n},+)\times(\mathbb{Z}_{m},+)\cong(\mathbb{Z}_{nm},+)$ -\end_inset - -. -\end_layout - -\begin_layout Enumerate -\begin_inset Argument item:1 -status open - -\begin_layout Plain Layout -\begin_inset Formula $\impliedby]$ -\end_inset - - -\end_layout - -\end_inset - -Sea +Si \begin_inset Formula $d:=\text{mcd}\{n,m\}>1$ \end_inset @@ -2636,6 +2604,38 @@ Sea no es cíclico. \end_layout +\begin_layout Enumerate +\begin_inset Argument item:1 +status open + +\begin_layout Plain Layout +\begin_inset Formula $\impliedby]$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Formula $G\cong(\mathbb{Z}_{n},+)$ +\end_inset + + y +\begin_inset Formula $H\cong(\mathbb{Z}_{m},+)$ +\end_inset + +, y por el teorema chino de los restos para anillos, +\begin_inset Formula $\mathbb{Z}_{n}\times\mathbb{Z}_{m}\cong\frac{\mathbb{Z}}{nm\mathbb{Z}}=\mathbb{Z}_{nm}$ +\end_inset + + como anillos, luego los grupos aditivos también son isomorfos y +\begin_inset Formula $G\times H\cong(\mathbb{Z}_{n},+)\times(\mathbb{Z}_{m},+)\cong(\mathbb{Z}_{nm},+)$ +\end_inset + +. +\end_layout + \end_deeper \begin_layout Enumerate Si |