Ejercicios T1

1 files changed, 68 insertions, 0 deletions

diff --git a/ealg/n1.lyx b/ealg/n1.lyx
index 0f5e52b..7434dd6 100644
--- a/ealg/n1.lyx
+++ b/ealg/n1.lyx
@@ -1087,6 +1087,9 @@ Si
 \end_inset
 
 .
+\end_layout
+
+\begin_layout Standard
 \begin_inset ERT
 status open
 
@@ -1227,6 +1230,38 @@ Dados
 \end_layout
 
 \begin_layout Standard
+Dados un dominio 
+\begin_inset Formula $D$
+\end_inset
+
+ de característica 0, 
+\begin_inset Formula $P\in D[X]\setminus\{0\}$
+\end_inset
+
+ y 
+\begin_inset Formula $a\in D$
+\end_inset
+
+, la multiplicidad de 
+\begin_inset Formula $a$
+\end_inset
+
+ en 
+\begin_inset Formula $P$
+\end_inset
+
+ es el menor 
+\begin_inset Formula $m\in\mathbb{N}_{0}$
+\end_inset
+
+ con 
+\begin_inset Formula $P^{(m)}(a)\neq0$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
 \begin_inset ERT
 status open
 
@@ -2126,6 +2161,27 @@ La irreducibilidad se conserva por automorfismos de dominios, por lo que
 \end_inset
 
 .
+ En 
+\begin_inset Formula $\mathbb{Z}[X]$
+\end_inset
+
+, 
+\begin_inset Formula $f:=X^{6}+X^{3}+1$
+\end_inset
+
+ es irreducible, pues 
+\begin_inset Formula $f(X+1)=X^{6}+6X^{5}+15X^{4}+21X^{3}+18X^{2}+9X+3$
+\end_inset
+
+ y, como este es irreducible por Eisenstein con 
+\begin_inset Formula $p=3$
+\end_inset
+
+, 
+\begin_inset Formula $f$
+\end_inset
+
+ es irreducible.
 \end_layout
 
 \begin_layout Standard
@@ -2272,6 +2328,18 @@ donde
 , etc.
 \end_layout
 
+\begin_layout Standard
+Para 
+\begin_inset Formula $n,m\in\mathbb{Z}^{+}$
+\end_inset
+
+, 
+\begin_inset Formula $\text{mcd}\{X^{n}-1,X^{m}-1\}=X^{\text{mcd}\{n,m\}}-1$
+\end_inset
+
+.
+\end_layout
+
 \begin_layout Section
 Factorización en 
 \begin_inset Formula $\mathbb{C}[X]$