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鐃緒申鐃緒申鐃緒申鐃緒申鐃� II 鐃緒申鐃緒申 No.8

鐃緒申鐃緒申鐃塾テ￥申鐃緒申:

\fbox{復習}鐃殉わ申鐃熟ワ申檗鐃緒申鐃緒申鐃緒申鐃塾駕申鐃緒申鐃祝つわ申鐃銃￥申

鐃緒申鐃緒申 6.1

$L={\Bbb C}(X,Y,Z), K={\Bbb C}(X+Y+Z,XY+YZ+ZX,XYZ)$ 鐃夙わ申鐃暑。鐃緒申鐃塾とわ申鐃緒申

1. $X$ 鐃緒申 $K$ 鐃緒申虜脳鐃渋随申犲逸申鐃緒申鐃淑わ申鐃緒申鐃緒申

2. $M=K(X)$ 鐃夙わ申鐃緒申鐃夙わ申鐃緒申 $[L:M], [M:K]$ 鐃薯それぞ鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

鐃殉わ申鐃緒申2. 鐃緒申 $[L:M]$ 鐃緒申 $[M:K]$ 鐃緒申鐃緒申鐃緒申鐃淑�鐃緒申鐃獣てわ申鐃淑わ申鐃処う鐃叔わ申鐃獣わ申鐃緒申 $[L:M]$ 鐃緒申鐃緒申鐃緒申鐃� $L$ 鐃緒申 $M$-鐃駿ワ申鐃夙ワ申鐃緒申屬箸鐃緒申討亮鐃緒申鐃緒申任鐃緒申辰董鐃緒申鐃緒申鐃緒申 鐃緒申鐃緒申鐃緒申鐃叔わ申鐃暑。鐃殉わ申鐃緒申鐃緒申鐃緒申鐃緒申鬚靴討鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃�

鐃緒申   $\mbox{${\Bbb Q}$ }[\sqrt{2}]$ 鐃緒申 $\mbox{${\Bbb Q}$ }$ 鐃緒申2鐃緒申鐃緒申鐃叔わ申鐃暑。鐃渋際￥申

\begin{displaymath}\mbox{${\Bbb Q}$}[\sqrt{2}]=\mbox{${\Bbb Q}$}+\mbox{${\Bbb Q}$}\sqrt{2} \end{displaymath}

鐃緒申鐃緒申他鐃緒申鐃緒申砲弔鐃緒申討鐃� No.4 鐃緒申鐃緒申鐃緒申鮖仮箸鐃緒申鐃緒申澆鐃緒申鐃緒申鐃�

鐃縦わ申鐃祝￥申鐃叔常申多鐃準式鐃夙鰹申鐃順次鐃緒申鐃塾ワ申鐃緒申澆任鐃緒申襪�鐃緒申 鐃緒申鐃緒申鐃� No.3 鐃祝わ申鐃暑。鐃緒申単鐃祝醐申鐃獣てわ申鐃殉わ申鐃出￥申

鐃緒申 $K$ 鐃緒申 $K$ 鐃緒申鐃緒申鐃重�鐃淑醐申 $x$ 鐃緒申鐃宿加わ申鐃緒申 $L=K(x)$ 鐃緒申鐃獣わ申鐃夙わ申鐃暑。 鐃盾し $x$ 鐃緒申 $K$ 鐃緒申虜脳鐃渋随申犲逸申亮鐃緒申鐃緒申鐃� $d$ 鐃叔わ申鐃緒申覆蕁� $[L:K]=d$ 鐃叔わ申鐃暑。

鐃夙わ申鐃緒申鐃緒申鐃夙になる。鐃緒申鐃緒申法鐃緒申造呂鐃緒申里箸鐃� $L=K[x]$ 鐃叔もあ鐃暑。鐃緒申鐃淑わ申鐃緒申鐃� $K$ 鐃緒申 $x$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃縦は実は種申動的鐃緒申鐃塾になわ申里鐃緒申鐃� 鐃緒申鐃緒申砲鐃� $x$ 鐃緒申 $K$ 鐃緒申鐃緒申鐃重�鐃叔わ申鐃暑こ鐃夙わ申鐃緒申鐃緒申鐃銃わ申鐃暑。

鐃緒申鐃緒申 6.2

鐃緒申鐃緒申鐃緒申鐃� 6.1鐃叔￥申 $L=K(X+cY)$ 鐃夙なわ申茲�鐃緒申 $c\in {\Bbb C}$ 鐃緒申鐃緒申 鐃緒申 (鐃緒申鐃緒申6.2 鐃塾常申鐃緒申鐃薯参考わ申)鐃緒申弔鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

鐃緒申鐃緒申鐃緒申鐃緒申鐃薯いのわ申 $c=1$ 鐃緒申 $c=0$ 鐃熟わ申鐃殉わ申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃夙わ申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申 鐃緒申鐃縦はわ申鐃緒申奮鐃緒申覆鐃緒申鐃緒申鐃書うまわ申鐃緒申鐃緒申鐃塾わ申鐃緒申鐃緒申鐃緒申砲鐃緒申鐃処う鐃緒申鐃緒申鐃緒申6.2鐃塾常申鐃緒申鐃緒申 鐃緒申鐃粛にわ申鐃銃わ申鐃緒申鐃緒申鐃緒申鐃宿わ申鐃緒け鐃緒申鐃緒申鐃緒申鐃緒申鐃塾よう鐃緒申 $c$ 鐃緒申直鐃旬醐申鐃縦わ申鐃暑こ鐃夙わ申任鐃緒申襦� 鐃緒申鐃緒申鐃祝なわ申里麓鐃緒申里鐃緒申箸任鐃緒申襦�(鐃出常申鐃緒申鐃薯うまわ申鐃緒申鐃術わ申鐃暑。)

$X+cY$ 鐃緒申 $f(T)\in K[T]$ 鐃塾駕申覆鐃出￥申$X+cZ$,$Y+cZ$,$Z+cY$,$Y+cX$,$Z+cX$鐃盾そ鐃緒申鐃叔わ申鐃暑。

鐃緒申鐃緒申 8.1   $L={\Bbb C}(X,Y,Z,W)$鐃夙わ申鐃緒申

\begin{displaymath}K=(\text{$(X,Y,Z,W)$の対称式であるような ${\Bbb C}$ 係数有理式全体}) \end{displaymath}

鐃夙わ申鐃暑。鐃緒申鐃塾とわ申鐃緒申$L$ 鐃緒申 $K$ 鐃夙わ申鐃緒申鐃緒申鐃�($K$ 鐃緒申泙鐃処う鐃緒申 $L$ 鐃緒申鐃緒申分鐃緒申 鐃緒申鐃緒申鐃緒申弔鐃緒申鐃緒申鐃緒申鐃緒申鐃� $K$ 鐃緒申粒鐃緒申膽￥申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申



2001-12-03