鐃緒申鐃緒申鐃�III 鐃緒申鐃緒申 No.12

鐃緒申鐃塾講居申鐃叔は￥申鐃塾と醐申鐃緒申鐃緒申 $\mbox{${\mathbb{Q}}$}$ 鐃緒申泙鐃緒申里鬚気鐃緒申鐃緒申箸鐃緒申鐃緒申佞鐃緒申討鐃緒申鐃緒申鐃�

鐃緒申鐃緒申 12.1 (鐃緒申鐃緒申鐃緒申鐃塾器申鐃緒申鐃緒申鐃緒申)

鐃緒申

鐃塾ワ申鐃緒申鐃緒申鐃緒申鐃緒申里箸鐃緒申鐃� $G=\operatorname{Gal}(L/K)$ 鐃夙わ申鐃緒申鐃夙￥申

$\displaystyle \mathcal G=\{$ $G$ 鐃緒申鐃緒申分鐃緒申 $\displaystyle \}$

鐃緒申

$\displaystyle \mathcal F=\{$ $L$ 鐃緒申 $K$ 鐃緒申鐃緒申鐃緒申鐃� $\displaystyle \}$

鐃塾わ申鐃緒申鐃緒申鐃祝は逸申鐃出逸申鐃出縁申鐃緒申鐃縦わ申鐃緒申鐃緒申鐃緒申鐃出縁申鐃熟￥申

$\displaystyle \Phi(H)=L^H$

$\displaystyle \Psi(M)=\operatorname{Gal}(L/M)$

鐃緒申与鐃緒申鐃緒申鐃暑。

鐃渋際には￥申鐃緒申鐃緒申弍鐃緒申蝋鐃緒申望椶鐃緒申鐃淑�申鐃緒申辰討鐃緒申董鐃� 鐃緒申鐃緒申鐃緒申鐃処い鐃緒申鐃緒申鐃緒申鐃緒申討鐃渋常申鐃緒申發緒申鐃緒申覆襦�申箸鐃緒申鐃緒申鐃緒申覆里任鐃緒申襪�申鐃� 鐃殉わ申鐃緒申鐃緒申弔里鐃塾わ申鐃出縁申鐃緒申鐃緒申箸鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬わ申鐃緒申鐃緒申鐃緒申

鐃緒申 12.1 $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 896 $ (\sqrt{2},\sqrt{3},\sqrt{5})$$ 鐃緒申 $\mbox{${\mathbb{Q}}$}$ 鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃�

$\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 901 $ (\sqrt{2},\sqrt{3},\sqrt{5})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 904 $ (\sqrt{2},\sqrt{3})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 907 $ (\sqrt{2},\sqrt{5})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 910 $ (\sqrt{3},\sqrt{5})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 913 $ (\sqrt{2})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 916 $ (\sqrt{3})$$ , $\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 919 $ (\sqrt{5})$$ , $\mbox{${\mathbb{Q}}$}$ 鐃緒申8鐃縦でわ申鐃暑。

鐃緒申 12.2 $\mbox{${\mathbb{Q}}$}$ 鐃緒申鐃� $% latex2html id marker 926 $ x=\sqrt{2}+\sqrt{3}+\sqrt{5}$$ 鐃塾最常申多鐃準式鐃塾種申鐃緒申鐃緒申

鐃叔わ申鐃緒申鐃粛緒申曚任鐃緒申襪�申鐃緒申鐃緒申両鐃緒申鐃緒申呂鐃緒申泙泙鐃�(半鐃出逸申鐃循のわ申鐃緒申鐃緒申) 鐃処伸鐃出わ申鐃祝わ申鐃緒申鐃処た鐃緒申鐃渋削申

鐃叔わ申鐃暑こ鐃夙わ申里鐃緒申鐃緒申里砲蓮鐃�

$\mbox{${\mathbb{Q}}$}$

鐃緒申鐃緒申鐃緒申个茲わ申鐃緒申鐃緒申鐃祝わ申

$\mbox{${\mathbb{Q}}$}$ $% latex2html id marker 940 $ (\sqrt{2},\sqrt{3},\sqrt{5})$$ 鐃淑わ申鐃塾わ申鐃緒申鐃重�申帽佑鐃緒申董鐃�

$\mbox{${\mathbb{Q}}$}$

鐃緒申鐃緒申鐃� $\mbox{${\mathbb{Q}}$}$

鐃緒申鐃緒申弔鐃緒申鐃緒申鐃緒申鐃夙になる。鐃緒申鐃峻わ申鐃緒申鐃重�申動廚任鐃緒申襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申討鐃緒申鐃緒申鐃� $\operatorname{Gal}(L/$ $\mbox{${\mathbb{Q}}$}$

鐃塾刻申造鐃緒申 ( $C_2\times C_2\times C_2$ 鐃緒申同鐃緒申鐃叔わ申鐃暑、鐃緒申鐃緒申鐃緒申鐃緒申鐃渋際の削申鐃緒申鐃緒申)鐃緒か鐃暑。鐃緒申鐃緒申鐃銃￥申

鐃緒申鐃緒申 ${\operatorname{id}}$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里匹慮鐃緒申任鐃緒申鐃緒申僂任覆鐃緒申鐃緒申箸鐃緒申蕁� $\mbox{${\mathbb{Q}}$}$

鐃緒申

鐃夙逸申鐃竣わ申鐃暑こ鐃夙わ申鐃緒か鐃暑。鐃緒申鐃緒申鐃塾わ申鐃夙はほとわ申鐃� 鐃重誌申鐃叔でわ申鐃緒申曚鐃緒申動廚雰彁鐃緒申燃里鐃緒申鐃緒申鐃暑。鐃緒申鐃曙が鐃緒申鐃緒申鐃緒申鐃緒申鐃塾逸申鐃熟でわ申鐃暑。

鐃緒申鐃緒申 12.1 有鐃緒申鐃緒申

鐃叔￥申

$\displaystyle \mbox{${\mathbb{Q}}$}$ $% latex2html id marker 968 $\displaystyle (a \sqrt{3}+b \sqrt{6})=$$ $\displaystyle \mbox{${\mathbb{Q}}$}$ $% latex2html id marker 970 $\displaystyle (\sqrt{2},\sqrt{3},\sqrt{6}) $$

鐃夙なわ申覆鐃緒申茲�申鐃�

鐃熟どのよう鐃淑わ申里鐃緒申鐃緒申鐃緒申撞鐃緒申覆鐃緒申鐃緒申鐃�