鐃緒申鐃緒申惘藹� I 鐃緒申鐃緒申 No.5

鐃緒申鐃緒申 5.1

鐃緒申 ${\mbox{${\mathbb{Z}}$}}$ 鐃塾ワ申鐃叔ワ申鐃緒申箸鐃緒申泙鐃緒申鐃緒申鐃緒申了鐃緒申鐃�

鐃緒申鐃塾醐申鐃叔￥申鐃緒申鐃緒申鐃塾随申鐃淑わ申弌鐃� 鐃緒申鐃叔鰹申辰鐃粛常申鐃� 鐃緒申鐃塾醐申鐃叔わ申鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申
鐃塾とわ申鐃緒申鐃緒申鐃緒申函鐃� 鐃塾醐申鐃緒申鐃緒申鐃緒申鐃緒申悩脳鐃緒申里鐃塾わ申存鐃淳わ申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃� 鐃夙わ申鐃緒申鐃夙￥申鐃緒申任鐃春の醐申鐃緒申鐃叔鰹申鐃緒申擇鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申
$I=a_0 {\mbox{${\mathbb{Z}}$}}$ 鐃薯示わ申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 5.2

鐃緒申 ${\mathbb{C}}[X]$ 鐃塾ワ申鐃叔ワ申鐃緒申箸鐃緒申泙鐃緒申鐃緒申鐃緒申了鐃緒申鐃�

鐃緒申鐃塾醐申鐃叔￥申鐃緒申 0 鐃叔なわ申鐃淑わ申弌鐃� 鐃緒申鐃叔鰹申辰鐃粛常申鐃� 鐃緒申鐃塾醐申鐃叔わ申鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申
鐃塾とわ申鐃緒申鐃緒申鐃緒申函鐃� 鐃塾醐申鐃緒申鐃緒申納鐃緒申鐃緒申鐃緒申脳鐃緒申里鐃塾わ申存鐃淳わ申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃� 鐃夙わ申鐃緒申鐃夙￥申鐃緒申任鐃春の醐申鐃緒申鐃叔鰹申鐃緒申擇鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申
$I=f_0 {\mathbb{C}}[X]$ 鐃薯示わ申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 5.3

$({\mbox{${\mathbb{Z}}$}},+)$ 鐃緒申鐃緒申分鐃緒申鐃緒申鐃緒申鐃緒申 ${\mbox{${\mathbb{Z}}$}}$ 鐃塾ワ申鐃叔ワ申鐃緒申任鐃緒申襪鰹申箸鮗┐鐃緒申覆鐃緒申鐃緒申鐃�
$({\mbox{${\mathbb{Z}}$}},+)$ 鐃緒申鐃緒申分鐃緒申鐃薯すべて居申鐃淑わ申鐃緒申鐃緒申
$({\mathbb{C}}[X],+)$ 鐃緒申鐃緒申分鐃緒申鐃叔￥申 ${\mathbb{C}}[X]$ 鐃塾ワ申鐃叔ワ申鐃緒申任呂覆鐃緒申鐃塾わ申鐃緒申鐃藷げなわ申鐃緒申鐃緒申

鐃緒申鐃緒申 5.4 $% latex2html id marker 1143 $ \omega=\frac{-1+\sqrt{-3}}{2}$$ (

鐃塾誌申鐃処根)鐃夙わ申鐃殉わ申鐃緒申鐃緒申鐃塾誌申鐃緒申

$% latex2html id marker 1147 $\displaystyle {\mbox{${\mathbb{Z}}$}}+{\mbox{${\mat... ...Z}}$}}\omega^2=\{a+b\omega+c\omega^2;\quad a,b,c \in {\mbox{${\mathbb{Z}}$}}\} $$

鐃緒申 ${\mathbb{C}}$ 鐃緒申鐃緒申分鐃縦でわ申鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申 (鐃緒申法鐃祝関わ申鐃緒申鐃緒申鐃緒申) 鐃緒申鐃塾環は￥申 ${\mbox{${\mathbb{Z}}$}}$ 鐃祝￥申 $\omega$ 鐃緒申鐃春わ申鐃獣わ申鐃緒申鐃縦になってわ申鐃暑。鐃緒申鐃緒申鐃叔￥申鐃緒申鐃塾環のわ申鐃夙わ申 ${\mbox{${\mathbb{Z}}$}}[\omega]$ 鐃夙わ申鐃緒申鐃緒申

鐃緒申鐃緒申 5.5

${\mbox{${\mathbb{Z}}$}}[\omega]$ (鐃緒申鐃巡参鐃緒申) 鐃緒申単鐃緒申鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�
$% latex2html id marker 1160 $ {\mbox{${\mathbb{Z}}$}}[\sqrt{3}]={\mbox{${\mathbb{Z}}$}}+{\mbox{${\mathbb{Z}}$}}\sqrt{3}$$ 鐃緒申単鐃緒申鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

鐃緒申鐃緒申 5.6

鐃緒申複鐃叔随申鐃夙わ申鐃殉わ申鐃緒申鐃緒申鐃塾とわ申鐃緒申

鐃緒申鐃術随申多鐃準式鐃緒申鐃叔鰹申辰鐃緒申箸鐃緒申鐃粛常申鐃緒申鐃叔わ申鐃暑こ鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申
${\mathbb{C}}[X]/(X-a){\mathbb{C}}[X]$ 鐃塾わ申鐃駿ての醐申鐃熟￥申鐃緒申鐃緒申複鐃叔随申 (鐃緒申同鐃緒申鐃緒申)鐃緒申鐃緒申鐃緒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

鐃緒申鐃出わ申鐃銃￥申鐃緒申鐃塾醐申鐃緒申鐃緒申分鐃祝わ申長鐃緒申鐃緒申佑鐃緒申襪鰹申箸鐃緒申任鐃緒申鐃� 鐃縮常申琉鐃縮ｏ申鐃緒申臓鐃緒申鐃緒申鐃緒申僂鐃�(鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃獣てわ申鐃緒申箸鐃緒申鐃緒申鐃緒申里鐃夙わ申) 鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申年鐃緒申鐃叔緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申覆鐃緒申鐃緒申分鐃緒申鐃緒申鐃塾まわ申鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申 5.7 ${\mbox{${\mathbb{Z}}$}}/15{\mbox{${\mathbb{Z}}$}}$ 鐃塾醐申鐃緒申鐃緒申分鐃祝わ申長鐃緒申鐃緒申鐃緒申

$\displaystyle \begin{pmatrix} 1& 2 & 3 \\ 4& 5 & 6 \end{pmatrix}\begin{pmatrix} 1& 2 & 3 \\ 4& 5 & 6\\ 7& 8 & 0\\ \end{pmatrix}$

鐃緒申彁鐃緒申鐃緒申鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申単鐃淑件申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃淑�申鐃緒申鐃緒申鐃緒申佑鐃� 14鐃淑駕申鐃緒申鐃緒申鐃緒申鐃祝わ申辰鐃宿緒申鐃緒申鐃銃わ申鐃緒申鐃緒申砲覆鐃処う鐃緒申直鐃緒申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 5.8 ${\mbox{${\mathbb{Z}}$}}/15{\mbox{${\mathbb{Z}}$}}$ 鐃塾醐申鐃緒申鐃緒申鐃叔にわ申長鐃緒申鐃�

$\displaystyle \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$

鐃緒申鐃緒申 5.9 ${\mbox{${\mathbb{Z}}$}}/14{\mbox{${\mathbb{Z}}$}}$ 鐃塾醐申鐃緒申鐃緒申鐃叔にわ申長鐃緒申鐃�

$\displaystyle \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{pmatrix}$

鐃緒申鐃緒申 5.10 ${\mbox{${\mathbb{Z}}$}}/16{\mbox{${\mathbb{Z}}$}}$ 鐃塾醐申鐃緒申鐃緒申鐃叔にわ申長鐃緒申鐃�

$\displaystyle \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{pmatrix}$

(鐃緒申鐃緒申琉焚鐃緒申鐃緒申鐃緒申鐃叔は刻申鐃藷式わ申肇譟種申鐃緒申鐃緒申鐃緒申鐃緒申鐃粛鰹申鐃緒申僂鐃緒申鐃緒申匹鐃緒申鐃�)

鐃緒申鐃緒申 5.11 ${\mbox{${\mathbb{Z}}$}}/15{\mbox{${\mathbb{Z}}$}}$ 鐃塾醐申鐃緒申鐃緒申鐃叔にわ申長鐃緒申鐃�

$\displaystyle A= \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{pmatrix}$

鐃塾逆刻申鐃緒申鐃渋醐申澆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申由鐃緒申鵑欧鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃� (鐃述ワ申鐃�:

鐃塾逆刻申鐃緒申

鐃緒申鐃緒申鐃獣わ申鐃夙わ申鐃暑。

(3鐃緒申鐃緒申単鐃縮刻申鐃緒申). 両鐃春わ申鐃緒申鐃藷式わ申箸鐃緒申...)

鐃緒申鐃緒申 5.12 鐃宿わ申鐃緒申鐃緒申鐃�

鐃緒申鐃出わ申鐃銃も、

$\displaystyle AB-BA=1_n$

鐃緒申澆鐃緒申鐃緒申鐃緒申鐃� $A,B \in M_n({\mathbb{C}})$ 鐃緒申存鐃淳わ申鐃淑わ申鐃緒申鐃夙を示わ申鐃淑わ申鐃緒申鐃緒申 (鐃述ワ申鐃�:鐃夙レー鐃緒申)

鐃緒申鐃緒申 5.13 鐃叔随申

鐃祝つわ申鐃銃￥申 $A,B\in M_p({\mathbb{F}}_p)$ 鐃叔￥申

$\displaystyle AB-BA=1_p$

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申鐃緒申鵑欧覆鐃緒申鐃緒申鐃� (鐃緒申鐃淑わ申鐃緒申鐃緒申任鐃緒申襦�

鐃塾とわ申鐃祝まわ申鐃庶し鐃銃みわ申鐃緒申匹鐃緒申鐃緒申鐃緒申里鐃淑わ申鐃緒申)