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鐃緒申鐃緒申鐃� II 鐃緒申鐃�

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塾わ申抜鐃緒申鐃緒申鐃銃わ申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃淳まわ申鐃緒申 鐃緒申鐃緒申鐃熟器申単鐃淑ので￥申鐃淑駕申鐃叔わ申略鐃准のみわ申颪い討鐃緒申鐃緒申泙鐃緒申鐃�

鐃緒申鐃緒申 0.1   鐃緒申 $k$ 鐃夙わ申鐃緒申有鐃渋種申鐃緒申鐃緒申鐃緒申 $L$ 鐃夙の間わ申鐃緒申鐃緒申鐃� $M$ 鐃緒申鐃出わ申鐃銃￥申

\begin{displaymath}[L:k]=[L:M][M:k] \end{displaymath}

鐃緒申鐃淑りた鐃縦￥申

[鐃緒申鐃緒申]

$[L:M]=e,[M:k]=f$ 鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申砲鐃所、
\begin{align*}&M=kv_1+kv_2+\dots+kv_f (\text{直和})\\ &L=Mw_1+Mw_2+\dots+Mw_e (\text{直和}) \end{align*}
鐃緒申澆鐃緒申鐃緒申茲�鐃緒申 $v_1,v_2,\dots,v_f\in M,w_1,w_2,\dots,w_e\in L$ 鐃緒申 存鐃淳わ申鐃暑。

\begin{displaymath}L=\sum_{ij} k\ w_iv_j \end{displaymath}

鐃緒申鐃淑りた鐃緒申鐃緒申鐃緒申鐃曙が直鐃渋でわ申鐃暑こ鐃夙もす鐃緒申鐃祝確わ申鐃緒申鐃緒申鐃塾で￥申$ef$ 鐃縦の醐申

\begin{displaymath}\{w_iv_j ;\ i=1,\dots,e,\ j=1,\dots,f\} \end{displaymath}

鐃緒申 $k$ 鐃緒申鐃� $L$ 鐃塾器申鐃緒申鐃粛随申鐃緒申討鐃緒申襪鰹申箸鐃淑�鐃緒申鐃暑。 鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃�

\begin{displaymath}[L:k]=ef=[L:M][M:k] \end{displaymath}

鐃緒申鐃緒申鐃緒申立鐃縦わ申鐃夙わ申分鐃緒申鐃暑。

鐃緒申鐃緒申鐃緒申鐃緒申鐃夙わ申鐃出￥申鐃純え鐃緒申 $\mbox{${\Bbb Q}$ }$ 鐃緒申 4鐃緒申鐃緒申鐃緒申 $L$ 鐃緒申 $\mbox{${\Bbb Q}$ }$ 鐃緒申3鐃緒申鐃緒申鐃緒申鐃� 鐃殉むこ鐃夙はなわ申鐃緒申鐃夙などわ申鐃緒か鐃緒申泙鐃緒申鐃�(鐃淑わ申鐃緒申鐃緒申鐃粛わ申鐃銃みてわ申鐃緒申鐃緒申鐃緒申鐃緒申)

鐃淑わ申鐃緒申No.11 鐃塾ワ申檗鐃緒申箸如鐃緒申磴�鐃緒申 $\alpha=\sqrt[3]{5},\quad \beta=\sqrt[3]{5}\omega$ 鐃祝わ申鐃緒申鐃緒申鐃銃￥申 $\mbox{${\Bbb Q}$ }[\alpha,\beta]=\mbox{${\Bbb Q}$ }[c\alpha+\beta]$鐃夙なわ申茲�鐃緒申 $c\in \mbox{${\Bbb Q}$ }$ 鐃緒申鐃緒申茵�鐃夙わ申鐃緒申鐃緒申鐃緒申砲弔鐃緒申董鐃� 鐃瞬居申鐃緒申鐃緒申鐃淑�鐃緒申鐃緒申覆鐃�(鐃緒申鐃緒申鐃銃わ申鐃獣てなわ申?)鐃緒申鐃初、鐃緒申鐃緒申鐃叔わ申鐃淑わ申鐃緒申鐃緒申 鐃緒申鐃緒申鐃緒申鐃緒申鐃粛わ申鐃緒申鐃殉わ申鐃緒申鐃緒申 鐃緒申鐃瞬んそのよう鐃淑人でも、

$\mbox{${\Bbb Q}$ }[\alpha,\beta]=\mbox{${\Bbb Q}$ }[2\alpha+\beta]$ 鐃薯示わ申

鐃夙わ申鐃緒申鐃緒申鐃緒申砲鐃緒申鐃出駕申鐃緒申鐃叔わ申鐃緒申鐃夙思わ申鐃殉わ申鐃緒申 鐃緒申鐃緒申辰箸鐃緒申鐃緒申佑鐃緒申鐃緒申鐃緒申儿鐃緒申如鐃緒申鐃緒申鐃緒申鐃緒申仆鐃叔わ申鐃緒申鐃緒申鐃所が 鐃薯けなわ申鐃塾はわ申辰鐃緒申鐃緒申覆鐃緒申辰任鐃緒申鐃�

鐃准器申鐃緒申文


 
Yoshifumi Tsuchimoto
2000-07-14