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zv$c6C|MD`*e9kGqY#l!prB;9Pxes%_&cyw33#_)$O?Un@dH~>vBD!w+4b6Hpy&;?S zZ$^W@#rUrSd7Y{MGrZW&PesxG<+Pa4tlcFFR>6ZjpVa^!8e^1_VwomK0G=_JU%uOi wK(KyK6obafhodZSnnRv+*l7Tc6n;V~aMO5O`U55hy7olq3=UAHI8j;s5{u diff --git a/TFG_Sixto_José_Martínez_Gan.tex b/TFG_Sixto_José_Martínez_Gan.tex index 7b8faf2..d83d87b 100644 --- a/TFG_Sixto_José_Martínez_Gan.tex +++ b/TFG_Sixto_José_Martínez_Gan.tex @@ -774,8 +774,9 @@ M^{***}\equiv\definicionconjunto{m \in \left( \dual{M} \right)_Q}{h\!\left( m \r \begin{definicion} - Sea $M$ un \modulo{A} finitamente generado. Diremos que $M$ tiene \emph{rango} $r$ si $M_Q$ es un \espaciovectorial{\cuerpofracciones{A}} de dimensión $r$.\todo{El rango de un ideal no nulo es $1$ aunque necesite más de un generador.} + Sea $M$ un \modulo{A} finitamente generado. Diremos que $M$ tiene \emph{rango} $r$ si $M_Q$ es un \espaciovectorial{\cuerpofracciones{A}} de dimensión $r$. \end{definicion} + Un caso particular importante es el de cualquier ideal $I$, que independientemente del número de generadores que tenga siempre es de rango $1$. \section{Producto Exterior} De cara a la demostración del Criterio de Saito, utilizaremos una operación que nos será de gran ayuda: el producto exterior. Para comprenderlo, necesitaremos entender primero el producto tensorial