diff options
Diffstat (limited to 'ac/n1.lyx')
| -rw-r--r-- | ac/n1.lyx | 200 |
1 files changed, 57 insertions, 143 deletions
@@ -2091,10 +2091,6 @@ status open . \end_layout -\begin_layout Subsection -Elementos primos e irreducibles -\end_layout - \begin_layout Standard \begin_inset ERT status open @@ -2435,39 +2431,7 @@ Si \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 Subsection -Dominios de factorización única -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -begin{reminder}{GyA} -\end_layout - -\end_inset - - +[...] \end_layout \begin_layout Standard @@ -3856,7 +3820,7 @@ end{exinfo} \end_layout -\begin_layout Subsection +\begin_layout Section Ideales finitamente generados \end_layout @@ -4039,80 +4003,6 @@ ideal principal \end_layout \begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -begin{exinfo} -\end_layout - -\end_inset - -Dado un anillo -\begin_inset Formula $A$ -\end_inset - - y -\begin_inset Formula $b\in A$ -\end_inset - - cancelable no invertible, -\begin_inset Formula $(b,X)$ -\end_inset - - no es un ideal principal de -\begin_inset Formula $A[X]$ -\end_inset - -, y en particular -\begin_inset Formula $(X,Y)$ -\end_inset - - no es un ideal principal de -\begin_inset Formula $A[X,Y]\coloneqq A[X][Y]$ -\end_inset - -. - Si -\begin_inset Formula $e\in A$ -\end_inset - - es idempotente, para -\begin_inset Formula $a\in A$ -\end_inset - -, -\begin_inset Formula $a\in(e)\iff a=ea$ -\end_inset - -, con lo que -\begin_inset Formula $(e)$ -\end_inset - - es un anillo con identidad -\begin_inset Formula $e$ -\end_inset - -. -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -end{exinfo} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard Un \series bold dominio de ideales principales @@ -4195,12 +4085,49 @@ begin{exinfo} \end_inset -En un DIP, -\begin_inset Formula $(a)+(b)=(\gcd\{a,b\})$ +Dado un anillo +\begin_inset Formula $A$ \end_inset y -\begin_inset Formula $(a)\cap(b)=(\text{lcm}\{a,b\})$ +\begin_inset Formula $b\in A$ +\end_inset + + cancelable no invertible, +\begin_inset Formula $(b,X)$ +\end_inset + + no es un ideal principal de +\begin_inset Formula $A[X]$ +\end_inset + +, y en particular +\begin_inset Formula $(X,Y)$ +\end_inset + + no es un ideal principal de +\begin_inset Formula $A[X,Y]\coloneqq A[X][Y]$ +\end_inset + +. + Si +\begin_inset Formula $e\in A$ +\end_inset + + es idempotente, para +\begin_inset Formula $a\in A$ +\end_inset + +, +\begin_inset Formula $a\in(e)\iff a=ea$ +\end_inset + +, con lo que +\begin_inset Formula $(e)$ +\end_inset + + es un anillo con identidad +\begin_inset Formula $e$ \end_inset . @@ -5332,7 +5259,16 @@ begin{exinfo} \end_inset -Dados un dominio +En un DIP, +\begin_inset Formula $(a)+(b)=(\gcd\{a,b\})$ +\end_inset + + y +\begin_inset Formula $(a)\cap(b)=(\text{lcm}\{a,b\})$ +\end_inset + +. + Dados un dominio \begin_inset Formula $A$ \end_inset @@ -6250,6 +6186,9 @@ característica . [...] La característica de un dominio no trivial es 0 o un número primo. +\end_layout + +\begin_layout Standard \begin_inset ERT status open @@ -6266,16 +6205,7 @@ end{reminder} \end_layout \begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -begin{samepage} -\end_layout - +\begin_inset Newpage pagebreak \end_inset @@ -6470,22 +6400,6 @@ status open \backslash -end{samepage} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash begin{exinfo} \end_layout @@ -9406,7 +9320,7 @@ coeficiente principal \series bold mónico \series default - si su coeficiente princial es 1. + si su coeficiente principal es 1. El polinomio 0 tiene grado \begin_inset Formula $-\infty$ \end_inset |