| 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 |
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| Line 36 $ab \in I$ $B$+$D(B $a\notin I$ $B$J$i$P(B $b \in |
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| $\sqrt{I} = \cap_{I\subset P:prime}P$ |
$\sqrt{I} = \cap_{I\subset P:prime}P$ |
| \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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