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version 1.1, 2000/03/01 02:25:51 version 1.3, 2000/03/28 02:02:30
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   %$OpenXM$
 \chapter{$B%$%G%"%k$NJ,2r(B}  \chapter{$B%$%G%"%k$NJ,2r(B}
 $B%$%G%"%k(B $I \subset R=K[X]$ $B$KBP$7(B, $I=I_1\cap I_2$ $B$H=q$1$k;~(B,  $B%$%G%"%k(B $I \subset R=K[X]$ $B$KBP$7(B, $I=I_1\cap I_2$ $B$H=q$1$k;~(B,
 $V(I) = V(I_1) \cup V(I_2)$ $B$,@.$jN)$D(B. $B$9$J$o$A(B, $B%$%G%"%k$NJ,2r(B  $V(I) = V(I_1) \cup V(I_2)$ $B$,@.$jN)$D(B. $B$9$J$o$A(B, $B%$%G%"%k$NJ,2r(B
Line 35  $ab \in I$ $B$+$D(B $a\notin I$ $B$J$i$P(B $b \in 
Line 36  $ab \in I$ $B$+$D(B $a\notin I$ $B$J$i$P(B $b \in 
 $\sqrt{I} = \cap_{I\subset P:prime}P$  $\sqrt{I} = \cap_{I\subset P:prime}P$
 \end{lm}  \end{lm}
 \proof $I \subset P$ $B$J$i$P(B $\sqrt{I} \subset \sqrt{P}=P$ $B$h$j(B  \proof $I \subset P$ $B$J$i$P(B $\sqrt{I} \subset \sqrt{P}=P$ $B$h$j(B
 $\subset$ $B$O(B OK. $B1&JU$,:8JU$r??$K4^$`$H$9$l$P(B, $B$"$k(B  $B:8JU(B $\subset$ $B1&JU(B. $B1&JU$,:8JU$r??$K4^$`$H$9$l$P(B, $B$"$k(B
 $f \in \cap_{I\subset P:prime}P \setminus \sqrt{I}$ $B$,B8:_$9$k(B. $B$3$N$H$-(B,  $f \in \cap_{I\subset P:prime}P \setminus \sqrt{I}$ $B$,B8:_$9$k(B. $B$3$N$H$-(B,
 $S=\{f,f^2,\cdots,\}$ $B$H$*$1$P(B,  $S=\{f,f^2,\cdots,\}$ $B$H$*$1$P(B,
 $S \cap \sqrt{I} = \emptyset$.  $S \cap \sqrt{I} = \emptyset$.

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