: 鐃緒申鐃緒申文鐃緒申砲弔鐃緒申鐃�...

鐃緒申鐃緒申惘藹� I 鐃緒申鐃緒申 No.10

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鐃緒申鐃緒申 10.1 単鐃準イ鐃叔ワ申鐃緒申鐃緒申鐃緒申

鐃塾醐申

鐃祝つわ申鐃銃￥申

鐃塾ワ申鐃叔ワ申鐃緒申

鐃熟￥申(

鐃緒申単鐃準イ鐃叔ワ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申蕁�)鐃緒申鐃緒申鐃縦の醐申

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襯わ申妊鐃緒申鐃�

鐃祝逸申鐃竣わ申鐃緒申筈鐃叔わ申鐃緒申鐃緒申鐃緒申

鐃緒申

鐃塾削申鐃緒申鐃緒申鷂気任鐃緒申襪鰹申函鐃緒申鐃緒申覆鐃緒申鐃緒申

鐃緒申鐃塾醐申鐃藷元でわ申鐃暑。(鐃縦まわ申鐃夙なわ申 $a',b'\in R$ 鐃緒申存鐃淳わ申鐃暑。)
$d'\in R$ 鐃緒申鐃塾醐申鐃藷元なわ申弌鐃� 鐃緒申鐃緒申鐃藷元でわ申鐃暑。

鐃夙わ申鐃緒申鐃緒申鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申鐃緒申鐃祝わ申蝓�縁申爛わ申妊鐃緒申鐃緒申鐃緒申鐃叔は￥申鐃緒申鐃緒申鐃緒申鷂気鐃緒申鐃緒申里箸鐃緒申鐃銃縁申佑飽鐃緒申鐃緒申泙鐃緒申鐃�

鐃緒申鐃緒申 10.2 $\alpha$ 鐃緒申 $% latex2html id marker 1012 $ {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}]$$ 鐃緒申鐃叔醐申鐃夙わ申鐃殉わ申鐃緒申鐃緒申鐃塾とわ申鐃緒申 $\vert\alpha\vert^2$ 鐃緒申鐃叔随申鐃緒申鐃緒申鐃叔随申鐃緒申2鐃処か鐃塾わ申鐃緒申鐃曙か鐃叔わ申鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申(鐃述ワ申鐃�:鐃叔随申 $p\in {\mbox{${\mathbb{Z}}$}}$ 鐃緒申 $\vert\alpha\vert^2$ 鐃緒申鐃緒申鐃緒申覆鐃出￥申 $p\vert\alpha\overline{\alpha}$ .

鐃緒申 $\alpha$ 鐃夙の削申鐃緒申鐃緒申鷂気鐃夙ってみなわ申鐃緒申鐃緒申)

鐃醇ー鐃緒申鐃緒申奪百弔砲鐃緒申鐃緒申討蓮鐃緒申團罅種申鐃緒申鐃獣ドの互緒申法鐃春にわ申辰萄鐃緒申鐃緒申鐃藷元わ申鐃緒申襪鰹申箸鐃緒申任鐃緒申泙鐃緒申鐃� 鐃緒申呂鐃祝種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 10.3 鐃緒申鐃塾器申

鐃緒申鐃緒申弔慮鐃緒申虜鐃緒申鐃緒申鐃緒申鐃緒申鐃醇ー鐃緒申鐃緒申奪匹慮濬鐃祝￥申砲鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

$R={\mbox{${\mathbb{Z}}$}}$ ;
$R={\mathbb{C}}[X]$ ; $X^{10}-1,X^{12}-1$

鐃緒申鐃緒申 10.1 $% latex2html id marker 1038 $ {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}]$$ 鐃祝わ申鐃緒申鐃銃￥申 $% latex2html id marker 1040 $ 3+4\sqrt{-1},15$$ 鐃塾削申鐃緒申鐃緒申鷂気鐃緒申鐃淑わ申鐃緒申鐃緒申

$% latex2html id marker 1042 $ \vert 15\vert=15>5=\vert 3+4\sqrt{-1}\vert$$ 鐃緒申鐃緒申鐃初、鐃殉わ申

鐃緒申 $% latex2html id marker 1046 $ 3+4\sqrt{-1}$$ 鐃叔鰹申辰討澆襦�

$% latex2html id marker 1048 $\displaystyle \frac{15}{3+4\sqrt{-1}}=\frac{9-12\sqrt{-1}}{5}=1.8-2.4\sqrt{-1} $$

鐃緒申鐃塾常申鐃祝わ申辰箸鐃潤い鐃塾わ申 $% latex2html id marker 1050 $ 2-2\sqrt{-1}$$ .

$% latex2html id marker 1052 $\displaystyle 10-(3+4\sqrt{-1})(2-2\sqrt{-1})=1-2\sqrt{-1} $$

鐃醇え鐃祝￥申

鐃緒申 $% latex2html id marker 1056 $ 3+4\sqrt{-1}$$ 鐃叔鰹申辰鐃緒申鐃粛常申鐃春わ申 $% latex2html id marker 1058 $ 1-2\sqrt{-1}$$ . 鐃緒申鐃緒申匹鐃� $% latex2html id marker 1060 $ 3+4\sqrt{-1}$$ 鐃緒申 $% latex2html id marker 1062 $ 1-2\sqrt{-1}$$ 鐃叔鰹申襦ｏ申鐃緒申鐃准わ申鐃塾で￥申鐃緒申鐃緒申鐃緒申 $% latex2html id marker 1064 $ 1-2\sqrt{-1}$$ .

鐃緒申鐃緒申 10.4 $% latex2html id marker 1067 $ {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}]$$ 鐃祝わ申鐃緒申鐃銃￥申鐃緒申鐃塾鰹申鐃夙の削申鐃緒申鐃緒申鷂気鐃緒申鐃淑わ申鐃緒申鐃緒申

$% latex2html id marker 1069 $ 12+36\sqrt{-1}$$ , $% latex2html id marker 1071 $ 5+13\sqrt{-1}$$
$% latex2html id marker 1073 $ 7+8\sqrt{-1}$$ ,

鐃緒申鐃緒申 10.5 $% latex2html id marker 1078 $ {\mbox{${\mathbb{Z}}$}}[\sqrt{-2}]$$ 鐃祝わ申鐃緒申鐃銃￥申鐃緒申鐃塾鰹申鐃夙の削申鐃緒申鐃緒申鷂気鐃緒申鐃淑わ申鐃緒申鐃緒申

$% latex2html id marker 1080 $ 2+3\sqrt{-2}$$ , $% latex2html id marker 1082 $ 11+22\sqrt{-2}$$
$% latex2html id marker 1084 $ 5+3\sqrt{-2}$$ ,

鐃緒申鐃緒申 10.6 $\mbox{${\mathbb{Q}}$}$

鐃塾種申鐃塾醐申鐃緒申鐃獣縁申砲鐃緒申覆鐃緒申鐃緒申鐃�

$\displaystyle \bar{X}^5+2\bar{X}^4+3\bar{X}+2$

鐃緒申鐃緒申 10.7 $\mbox{${\mathbb{Q}}$}$

鐃塾醐申 $\bar{X}^{100}$ 鐃緒申鐃獣縁申砲鐃緒申覆鐃緒申鐃緒申鐃�

鐃緒申鐃緒申 10.8 鐃緒申 $\mbox{${\mathbb{Q}}$}$

鐃塾醐申 $a \bar{X}+b$ ( $a,b\in$ $\mbox{${\mathbb{Q}}$}$ , $% latex2html id marker 1109 $ (a,b)\neq (0,0)$$ ) 鐃塾逆醐申鐃緒申(鐃緒申鐃曙が存鐃淳わ申鐃緒申鐃緒申砲鐃�)鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃塾環わ申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申 10.9 鐃緒申 $\mbox{${\mathbb{Q}}$}$

鐃塾醐申 $a \bar{X}+b$ ( $a,b\in$ $\mbox{${\mathbb{Q}}$}$ , $% latex2html id marker 1120 $ (a,b)\neq (0,0)$$ ) 鐃塾逆醐申鐃緒申(鐃緒申鐃曙が存鐃淳わ申鐃緒申鐃緒申砲鐃�)鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃塾環わ申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申 10.10 ${\mbox{${\mathbb{Z}}$}}[X]/(X^2-5)$ 鐃塾醐申 $(\bar{X}+1)^3$ 鐃緒申鐃獣縁申砲鐃緒申覆鐃緒申鐃緒申鐃�

鐃緒申鐃緒申 10.11

鐃淑随申 $123456789 (10)= 1\times 10^8+2\times 10^7+3\times 10^6+4\times 10^5 +5\times 10^4+6\times 10^3+7\times 10^2+8\times 10^1+9$ 鐃緒申鐃叔鰹申辰鐃粛常申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申
鐃淑随申 $135246 (7)= 1\times 7^5+3\times 7^4+5\times 7^3+ 2\times 7^2+4\times 7+6$ 鐃緒申鐃叔鰹申辰鐃粛常申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�
鐃淑随申

147ad258be369cf $\displaystyle (16)$

$\displaystyle (=$ $\displaystyle 1 \cdot 16^{14}+4 \cdot 16^{13}+7 \cdot 16^{12}+10\cdot 16^{11}+ 13\cdot 16^{10}+2 \cdot 16^9 +5 \cdot 16^8$

$\displaystyle +$ $\displaystyle 8\cdot 16^7 + 11\cdot 16^6 +14\cdot 16^5 +3 \cdot 16^4 +6\cdot 16^3+ 9\cdot 16^2 + 12\cdot 16 +15 )$

鐃緒申鐃叔鰹申辰鐃粛常申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�(a=10,b=11,c=12,d=13,e=14,f=15; 鐃緒申鐃緒申團紂種申鐃� 鐃緒申鐃緒申鐃緒申鐃叔わ申 147ad258be369cf 鐃塾わ申鐃夙わ申 147ad258be369cfh 鐃夙わ申 0x147ad258be369cf 鐃夙書きまわ申鐃緒申
多鐃準式 $X^{14}+3X^5+7X^2+8$ 鐃緒申鐃叔鰹申辰鐃粛常申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

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平鐃緒申19年12鐃緒申7鐃緒申

	147ad258be369cf $\displaystyle (16)$
$\displaystyle (=$	$\displaystyle 1 \cdot 16^{14}+4 \cdot 16^{13}+7 \cdot 16^{12}+10\cdot 16^{11}+ 13\cdot 16^{10}+2 \cdot 16^9 +5 \cdot 16^8$
$\displaystyle +$	$\displaystyle 8\cdot 16^7 + 11\cdot 16^6 +14\cdot 16^5 +3 \cdot 16^4 +6\cdot 16^3+ 9\cdot 16^2 + 12\cdot 16 +15 )$