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: 鐃緒申鐃緒申文鐃緒申砲弔鐃緒申鐃�...

    

鐃緒申鐃緒申鐃�III 鐃緒申鐃緒申 No.6

鐃緒申鐃緒申鐃塾テ￥申鐃緒申

\fbox{単純拡大の重要性・復習 I}

鐃緒申鐃緒申泙任暴劼戮鐃緒申茲�鐃祝￥申 鐃緒申 $ K$ 鐃緒申鐃縦わ申鐃緒申鐃重�鐃淑醐申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃処う鐃緒申鐃緒申 $ K(\alpha)$ 鐃熟￥申$ \alpha$ 鐃塾最常申多鐃準式 $ m(X)$ 鐃緒申鐃術わ申鐃緒申 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申 $ K[X]/m(X)K[X]$ 鐃緒申同鐃緒申鐃叔わ申鐃所、鐃緒申鐃緒申鐃緒申僂鐃緒申董峩鐃緒申鐃竣わ申 鐃緒申念鐃緒申鐃緒申立鐃緒申鐃緒申襪鰹申箸砲覆鐃緒け鐃緒申鐃緒申鐃緒申$ K$ 鐃緒申複鐃緒申鐃塾醐申鐃緒申鐃春わ申鐃獣わ申鐃緒申鐃緒申鐃緒申 鐃宿わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襦�

鐃緒申鐃緒申 6.1   $ K$ 鐃緒申有鐃緒申鐃緒申鐃緒申 $ \mbox{${\mathbb{Q}}$}$ 鐃緒申鐃緒申分鐃塾に誌申鐃縦よう鐃緒申鐃塾でわ申鐃緒申箸鐃緒申襦� $ K$ 鐃緒申鐃緒申鐃重�鐃淑醐申 $ \alpha,\beta$ 鐃祝わ申鐃緒申鐃緒申鐃銃￥申

$\displaystyle K(\alpha,\beta)=K(\alpha+c \beta) $

鐃緒申鐃緒申鐃緒申鐃緒申鐃処う鐃緒申 $ c\in K$ 鐃緒申存鐃淳わ申鐃暑。(鐃渋は￥申鐃緒申辰閥鐃緒申鐃緒申鐃緒申鐃緒申 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃処う鐃緒申 $ c\in K$ 鐃緒申有鐃渋個わ申鐃緒申鐃淑わ申鐃夙わ申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃暑。)

鐃緒申鐃緒申 4.1[鐃銃件申] 鐃祝つわ申鐃銃￥申

$ \mbox{${\mathbb{Q}}$}$$ [X]$ 鐃塾醐申 $ f_1,f_2,f_3,f_4,f_5$ 鐃叔￥申 % latex2html id marker 727 $ a=\sqrt{2}+\sqrt{3}$ 鐃祝わ申鐃緒申鐃緒申鐃緒申 $ f_1(a)=f_2(a)=f_3(a)=f_4(a)=f_5(a)$ 鐃緒申 鐃緒申鐃緒申鐃緒申鐃処う鐃淑わ申里鮓�つわ申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申鐃緒申鐃緒申呂笋居申鐃緒申鐃緒申里任鐃緒申襪�鐃緒申鐃緒申鐃緒申鐃緒申鐃旬わ申鐃獣わ申鐃塾で駕申鐃盾す鐃暑。

鐃緒申鐃緒申 6.1  

   $\displaystyle \mbox{${\mathbb{Q}}$}$% latex2html id marker 733 $\displaystyle (\sqrt{2}+\sqrt{3}+\sqrt{5})=$   $\displaystyle \mbox{${\mathbb{Q}}$}$% latex2html id marker 735 $\displaystyle (\sqrt{2},\sqrt{3},\sqrt{5}) $

鐃緒申鐃緒申鐃緒申立鐃縦わ申鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 6.2   $ \mbox{${\mathbb{Q}}$}$ 鐃緒申鐃緒申鐃重�鐃淑醐申 $ \alpha,\beta$ 鐃叔￥申

   $\displaystyle \mbox{${\mathbb{Q}}$}$% latex2html id marker 743 $\displaystyle (\alpha+\beta) \neq$   $\displaystyle \mbox{${\mathbb{Q}}$}$$\displaystyle (\alpha,\beta) $

鐃叔わ申鐃緒申茲�鐃淑わ申里鐃緒申鐃緒申鵑欧覆鐃緒申鐃緒申鐃�


平鐃緒申16年5鐃緒申25鐃緒申