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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�II 鐃緒申鐃緒申 No.1

鐃緒申鐃緒申鐃塾テ￥申鐃緒申:

\fbox{環と体の定義の復習。記号の約束 環 ${\mbox{${\Bbb Z}$}}$、 ${\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}$}

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申法鐃緒申鐃緒申旅峙鐃緒申鐃緒申鐃殉わ申鐃淑わ申鐃初す鐃緒申鐃祝つわ申鐃銃書いてわ申鐃緒申鐃緒申

鐃緒申鐃塾講居申鐃塾種申鐃緒申鐃粛�鐃緒申鐃緒申(鐃緒申鐃叔の随申鐃緒申有鐃渋個でわ申鐃緒申茲�鐃緒申鐃緒申)鐃叔わ申鐃暑。

鐃殉わ申鐃緒申鐃縦わ申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟わ申董鐃� 有鐃緒申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃夙緒申鐃緒申鐃緒申鐃緒申調鐃駿る。 鐃縦わ申鐃塾わ申鐃緒申鐃緒申砲弔鐃緒申討禄鐃緒申鐃緒申鐃�2鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申悗燃悗鐃緒申鐃熟わ申鐃叔はわ申鐃暑が鐃緒申 鐃緒申鐃緒申鮨┐襪鰹申箸砲鐃緒申呂鐃緒申鐃緒申鐃緒申琉鐃縮ｏ申覆匹鐃淑�鐃緒申鐃暑こ鐃夙わ申多鐃緒申鐃緒申鐃夙と思わ申鐃緒申

鐃縦わ申鐃緒申多鐃準式鐃熟の駕申慮朕鐃緒申函鐃緒申鐃緒申鐃緒申鐃緒申曚鐃緒申討鐃緒申鐃緒申鐃舜随申(鐃緒申鐃緒申鐃緒申鐃醇ゼ鐃緒申鐃緒申鐃舜随申) 鐃祝つわ申鐃銃述べる。鐃緒申鐃緒申鐃緒申鐃醇ゼ鐃緒申鐃緒申鐃舜随申鐃祝つわ申鐃銃は極わ申匿鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申辰董鐃� 鐃緒申鐃緒申鐃叔はわ申鐃緒申鐃述介するこ鐃夙はでわ申鐃淑わ申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃初い鐃殉でわ申 鐃緒申鐃緒申任鐃緒申襪�鐃緒申鐃塾わ申覆鐃緒申鐃�

鐃叔はまわ申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃熟わ申茲�鐃緒申鐃緒申鐃緒申的鐃祝わ申鐃緒申鐃緒申判劼戮鐃緒申鐃緒申鐃薯してわ申鐃緒申覆鐃� 鐃緒申鐃緒申多鐃緒申鐃塾で￥申鐃殉わ申鐃緒申鐃緒申鐃緒申擇鐃緒申鐃緒申鬚靴鐃縦削申鐃緒申鐃緒申鐃緒申鐃�

鐃緒申鐃� 1.1  
  1. 鐃縦とは￥申鐃緒申鐃塾なわ申鐃緒申鐃渋￥申鐃緒申鐃緒申鐃術わ申鐃緒申由鐃祝行わ申鐃緒申茲�鐃淑緒申鐃緒申任鐃緒申襦�
  2. 鐃塾とは￥申鐃緒申鐃塾なわ申鐃緒申鐃渋￥申鐃緒申鐃緒申鐃術わ申鐃緒申鐃� 0 鐃淑鰹申鐃塾醐申鐃祝わ申鐃緒申蟷誌申鐃� 鐃緒申由鐃祝行わ申鐃緒申茲�鐃淑緒申鐃緒申任鐃緒申襦�

鐃緒申鐃塾講居申鐃叔使わ申鐃縦は￥申単鐃縮醐申 $ 1$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃祝￥申鐃緒申調鐃緒申覆鐃緒申(鐃縦器申鐃緒申)鐃叔わ申鐃暑。 鐃塾も、鐃緒申法鐃緒申鐃縦器申鐃淑わ申鐃�(鐃縦器申鐃緒申)鐃塾みを扱わ申鐃緒申 鐃淑後、鐃獣わ申鐃叔わ申覆鐃緒申造蝓�鐃縦わ申鐃塾と醐申鐃緒申鐃出わ申鐃塾よう鐃淑わ申里鐃舜わ申鐃緒申里鐃緒申鐃緒申鬚気譴随申鐃緒申鐃�

鐃縦わ申鐃緒申鐃塾わ申鐃緒申鐃緒申麓鐃緒申里茲�鐃祝なわ申.

鐃緒申鐃� 1.2 (鐃縦わ申鐃緒申鐃塾わ申鐃緒申鐃�)   鐃緒申鐃緒申 $ R$ 鐃緒申鐃縦でわ申鐃緒申箸蓮鐃渋�鐃緒申鐃緒申鐃夙呼ばわ申鐃緒申鐃緒申

$\displaystyle +: R\times R \to R $

鐃夙掛わ申鐃緒申鐃夙呼ばわ申鐃緒申鐃緒申

$\displaystyle \times :R\times R \to R $

鐃緒申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃銃種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祝醐申鐃緒申鐃緒申
  1. $ R$ 鐃緒申足鐃緒申鐃緒申鐃祝関わ申鐃銃可器申鐃緒申鐃緒申覆鐃緒申鐃�
  2. $ R$ 鐃緒申鐃術は件申鐃祝‖э申鐃緒申鐃緒申鐃緒申鐃緒申鐃�
  3. $ R$ 鐃緒申足鐃緒申鐃緒申鐃夙掛わ申鐃緒申鐃緒申分鐃緒申法則鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申
  4. $ R$ 鐃緒申鐃術に関わ申鐃緒申単鐃縮醐申鐃緒申鐃緒申帖鐃�

忘鐃曙た鐃粛わ申2鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申悗旅峙鐃緒申鐃緒申鐃暑か鐃緒申鐃旬講居申鐃塾誌申鐃粛緒申

鐃瞬件申鐃緒申鐃縦￥申鐃緒申鐃緒申鐃緒申弯鐃緒申聞鐃緒申鐃緒申鐃渋偲�鐃緒申鐃緒申(鐃緒申立鐃緒申鐃緒申)

鐃淑どを参考にわ申鐃緒申箸茲わ申鐃緒申覆鐃緒申鐃緒申綉�鐃緒申鐃旬はよい鐃旬ではわ申鐃暑が鐃緒申 鐃旬講居申鐃夙居申鐃醇が鐃緒申弔鐃緒申鐃緒申曚覆鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申楾峙鐃緒申鐃� $ {\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}$ 鐃夙呼ぶ環のわ申鐃夙わ申 鐃遵記鐃緒申鐃旬ではわ申鐃出わ申鐃緒申 $ {\mbox{${\Bbb Z}$}}_n$ 鐃夙書いてわ申鐃暑。 鐃旬講居申鐃叔は居申鐃緒申 $ {\mbox{${\Bbb Z}$}}_n$ 鐃熟使わ申覆鐃� (鐃旬講居申鐃叔は使わ申覆鐃緒申鐃� $ {\mbox{${\Bbb Z}$}}_n$ 鐃祝は上記鐃夙わ申鐃緒申鐃緒申鐃縮の逸申味鐃緒申鐃緒申鐃暑。) 鐃塾わ申鐃緒申鐃春わ申鐃曙た鐃緒申鐃緒申

鐃縦わ申鐃緒申箸鐃緒申討蓮鐃緒申泙鐃緒申鐃緒申鐃緒申鐃緒申里里覆鐃緒申鐃� $ {\mbox{${\Bbb Z}$}}$ 鐃緒申鐃緒申鐃暑。 鐃盾う鐃緒申弔鐃緒申鐃緒申 $ {\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}$ 鐃叔わ申鐃暑。鐃緒申鐃緒申蓮鐃� $ {\mbox{${\Bbb Z}$}}$ 鐃薯そのワ申鐃叔ワ申鐃緒申 $ n{\mbox{${\Bbb Z}$}}$ 鐃叔鰹申辰鐃� 鐃緒申余鐃縦でわ申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申茲�鐃緒申 鐃緒申鐃緒申 $ x,y$ 鐃緒申鐃出わ申鐃緒申,

$\displaystyle x$    鐃緒申 $\displaystyle y$    鐃夙わ申同鐃緒申鐃緒申鐃初ス% latex2html id marker 850 $\displaystyle \quad {\Leftrightarrow}\quad x-y\in n{\mbox{${\Bbb Z}$}} $

鐃夙わ申鐃緒申襪鰹申箸鐃� $ {\mbox{${\Bbb Z}$}}$ 鐃祝￥申$ n$ 鐃緒申法鐃夙わ申鐃緒申鐃緒申鐃初ス分鐃緒申鐃緒申曚匹鐃緒申鐃緒申鐃� $ [x]_n$ 鐃緒申 鐃緒申$ x$ 鐃緒申 $ n$ 鐃緒申法鐃夙わ申鐃緒申鐃緒申鐃初ス鐃竣と件申瓩随申箸鐃緒申鐃� 鐃緒申鐃緒申箸鐃緒申董鐃�

$\displaystyle {\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}=\{ [x]_n ; x \in {\mbox{${\Bbb Z}$}}\} $

鐃緒申鐃緒申鐃緒申鐃緒申襦� $ {\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}$ 鐃祝は駕申法鐃緒申鐃緒申法鐃緒申鐃緒申

% latex2html id marker 866 $\displaystyle [a]_n+[b]_n=[a+b]_n, \quad [a]_n+[b]_n=[a+b]_n $

鐃叔わ申鐃殉わ申鐃緒申鐃緒申鐃緒申譟�鐃緒申鐃塾演算鐃祝わ申辰鐃� $ {\mbox{${\Bbb Z}$}}/n{\mbox{${\Bbb Z}$}}$ 鐃熟環になわ申里任鐃緒申襦� 鐃淑わ申鐃緒申鐃瞬わ申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃竣とわ申鐃緒申鐃緒申鐃春は逸申達鐃叔はなわ申鐃緒申 鐃処い鐃緒申鐃初ス分鐃緒申鐃緒申分鐃緒申鐃淑わ申鐃夙わ申鐃殉わ申鐃緒申法鐃緒申鐃緒申法鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申箸聾造鐃淑わ申鐃塾でわ申鐃暑。 鐃緒申鐃緒申鮖仮箸里鐃緒申鐃�

鐃緒申鐃緒申 1.1   $ {\mbox{${\Bbb Z}$}}$ 鐃祝ワ申鐃初ス分鐃緒申鐃緒申

$\displaystyle x$    鐃緒申 $\displaystyle y$    鐃夙わ申同鐃緒申鐃緒申鐃初ス% latex2html id marker 875 $\displaystyle \quad {\Leftrightarrow}\quad \vert x\vert=\vert y\vert $

鐃叔件申瓩随申箸鐃緒申襦� $ x$ 鐃塾わ申鐃塾ワ申鐃初ス分鐃緒申鐃祝わ申襯�鐃初ス鐃緒申 $ [x]$ 鐃夙書き￥申 $ {\mbox{${\Bbb Z}$}}$ 鐃薯このワ申鐃初ス分鐃緒申鐃緒申分鐃緒申鐃緒申鐃緒申鐃初ス鐃緒申鐃緒申鐃塾わ申 $ A$ 鐃夙書くわ申鐃夙にわ申鐃暑。鐃緒申鐃塾とわ申鐃緒申
  1. $ [x][y]$=$ [xy]$ 鐃祝わ申辰鐃� $ A$ 鐃祝は常申法鐃緒申鐃緒申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃暑こ鐃夙を示わ申鐃緒申
  2. $ [x]+[y]=[x+y]$ 鐃祝わ申辰討鐃� $ A$ 鐃祝は駕申法鐃緒申鐃緒申鐃殉わ申 鐃緒申鐃�鐃緒申鐃緒申覆鐃�鐃緒申鐃夙を示わ申鐃緒申

鐃銃駕申鐃緒申鐃緒申鐃熟ワ申檗鐃緒申箸鐃緒申鐃出わ申鐃暑こ鐃夙￥申鐃緒申个鐃緒申辰忙鐃緒申蠅件申覆鐃緒申造鐃� 鐃緒申鐃緒申旅峙鐃緒申僚鐃塾誌申鐃緒申屬帽圓鐃緒申鐃塾とわ申鐃暑。(鐃緒申鐃緒申鐃緒申遜鐃緒申覆鼻鐃緒申鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申砲鐃� 鐃緒申鐃塾旨告げわ申仄鐃緒申鐃緒申鐃緒申泙鐃緒申鐃�)


2002年5鐃緒申22鐃緒申