Añadido sobre números primos e irreducibles

1 files changed, 153 insertions, 12 deletions

diff --git a/ac/n1.lyx b/ac/n1.lyx
index 4d02078..488d056 100644
--- a/ac/n1.lyx
+++ b/ac/n1.lyx
@@ -972,6 +972,35 @@ idempotente
 \end_layout
 
 \begin_layout Standard
+Dado un homomorfismo 
+\begin_inset Formula $f:A\to B$
+\end_inset
+
+, si 
+\begin_inset Formula $a\in A$
+\end_inset
+
+ es invertible, nilpotente o idempotente, también lo es 
+\begin_inset Formula $f(a)\in B$
+\end_inset
+
+.
+ Si además 
+\begin_inset Formula $f$
+\end_inset
+
+ es inyectivo, si 
+\begin_inset Formula $f(a)\in B$
+\end_inset
+
+ es cancelable, nilpotente o idempotente, también lo es 
+\begin_inset Formula $a\in A$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
 Dados anillos 
 \begin_inset Formula $A_{1},\dots,A_{n}$
 \end_inset
@@ -1795,36 +1824,148 @@ status open
 \end_layout
 
 \begin_layout Standard
-Dado un dominio 
-\begin_inset Formula $D$
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{reminder}{GyA}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sean 
+\begin_inset Formula $A$
+\end_inset
+
+ un anillo [...] y 
+\begin_inset Formula $a\in A\setminus(A^{*}\cup\{0\})$
 \end_inset
 
 , 
-\begin_inset Formula $a\in D\setminus(D^{*}\cup\{0\})$
+\begin_inset Formula $a$
 \end_inset
 
  es 
 \series bold
 irreducible
 \series default
- si para 
-\begin_inset Formula $b,c\in D$
+ en 
+\begin_inset Formula $A$
 \end_inset
 
- con 
-\begin_inset Formula $a=bc$
+ si 
+\begin_inset Formula $\forall b,c\in A,(a=bc\implies b\in A^{*}\lor c\in A^{*})$
 \end_inset
 
-, 
-\begin_inset Formula $b\in D^{*}$
+, y es 
+\series bold
+primo
+\series default
+ en 
+\begin_inset Formula $A$
 \end_inset
 
- o 
-\begin_inset Formula $c\in D^{*}$
+ si 
+\begin_inset Formula $\forall b,c\in A,(a\mid bc\implies a\mid b\lor a\mid c)$
 \end_inset
 
 .
- Un 
+\end_layout
+
+\begin_layout Standard
+Si 
+\begin_inset Formula $A$
+\end_inset
+
+ es un dominio, todo primo es irreducible.
+\end_layout
+
+\begin_layout Standard
+Irreducible en un dominio no implica primo.
+ [...]
+\end_layout
+
+\begin_layout Standard
+Dados un anillo [...] 
+\begin_inset Formula $A$
+\end_inset
+
+ y 
+\begin_inset Formula $S\subseteq A$
+\end_inset
+
+, 
+\begin_inset Formula $a\in A$
+\end_inset
+
+ es un 
+\series bold
+máximo común divisor
+\series default
+ de 
+\begin_inset Formula $S$
+\end_inset
+
+ en 
+\begin_inset Formula $A$
+\end_inset
+
+, 
+\begin_inset Formula $a=\text{mcd}S$
+\end_inset
+
+, si divide a cada elemento de 
+\begin_inset Formula $S$
+\end_inset
+
+ y es múltiplo de cada elemento que cumple esto, y es un 
+\series bold
+mínimo común múltiplo
+\series default
+ de 
+\begin_inset Formula $S$
+\end_inset
+
+ en 
+\begin_inset Formula $A$
+\end_inset
+
+, 
+\begin_inset Formula $a=\text{mcm}S$
+\end_inset
+
+, si es múltiplo de cada elemento de 
+\begin_inset Formula $S$
+\end_inset
+
+ y divide a cada elemento que cumple esto.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{reminder}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Un 
 \series bold
 dominio de factorización única
 \series default