鐃緒申鐃緒申鐃�II鐃緒申鐃緒申 No.10

鐃緒申鐃緒申 10.1 $Z({\mathbb{C}}[G])$ 鐃祝わ申鐃緒申鐃緒申鐃緒申(0 鐃淑鰹申鐃緒申)鐃緒申鐃緒申鐃緒申鐃緒申存鐃淳わ申鐃淑わ申鐃緒申鐃夙わ申鐃祝￥申 $Z({\mathbb{C}}[G])$ 鐃緒申任鐃春の醐申

鐃緒申鐃出わ申鐃銃￥申

鐃緒申鐃緒申鐃緒申鐃緒申 ${\mathbb{C}}$ 鐃緒申鐃� 多鐃準式鐃叔種申鐃緒申鐃緒申鐃叔常申鐃塾わ申鐃�(鐃叔常申多鐃準式) 鐃熟重削申鐃緒申發随申覆鐃緒申鐃�

鐃緒申鐃� 10.1 鐃緒申

鐃緒申鐃緒申分鐃緒申鐃緒申

鐃緒申

鐃塾削申鐃緒申鐃叔ワ申鐃緒申任鐃緒申鐃夙は￥申

鐃緒申鐃緒申鐃塾常申鐃緒申鐃緒申足鐃緒申鐃緒申箸鐃緒申砲鐃緒申鐃緒申鐃�

$0 \in J$
$x,y\in J \implies x+ y, x-y \in J$
$r\in R$ , $x\in J$ $\implies$ $rx\in J$

鐃緒申鐃緒申鐃旬の常申鐃薯、種申鐃塾常申鐃緒申鐃瞬わ申鐃緒申鐃緒申鐃銃縁申鐃緒申鐃叔ワ申鐃緒申鐃緒申鐃緒申鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。

$r\in R$ , $x\in J$ $\implies$ $xr\in J$

鐃緒申(両側)鐃緒申鐃叔ワ申鐃緒申箸蓮鐃� 鐃塾削申鐃緒申鐃叔ワ申鐃暑か鐃縦縁申鐃緒申鐃叔ワ申鐃緒申砲覆辰討鐃緒申鐃処う鐃緒申鐃緒申痢鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃出常申鐃�(1),(2),(3)鐃緒申鐃緒申同鐃緒申鐃祝みわ申鐃緒申鐃処う鐃淑わ申里里鐃緒申箸任鐃緒申襦�

鐃緒申鐃緒申 10.2 $Z({\mathbb{C}}[G])$ 鐃塾醐申

鐃祝わ申鐃緒申鐃緒申鐃緒申 ${\mathbb{C}}[G]$ 鐃緒申

鐃塾醐申有鐃緒申鐃瞬わ申直鐃渋わ申(鐃獣件申鐃夙わ申鐃緒申) 分鐃薯し￥申鐃緒申鐃緒申砲鐃緒申譴常申鐃塾醐申有鐃緒申鐃瞬わ申 ${\mathbb{C}}[G]$ 鐃緒申(両側)鐃緒申鐃叔ワ申鐃緒申砲覆襦� 鐃緒申辰醗鐃緒申未法鐃� $Z({\mathbb{C}}[G])$ 鐃緒申有鐃渋個の醐申 $z_1,z_2,\dots,z_l$ 鐃祝わ申鐃緒申鐃緒申鐃緒申 ${\mathbb{C}}[G]$ 鐃緒申 $z_1,z_2,\dots,z_l$ 鐃緒申同鐃緒申鐃緒申有鐃緒申鐃緒申(鐃緒申鐃曙ぞ鐃緒申慮鐃粛㍼申鐃緒申屬龍鐃緒申鐃緒申鐃淑�) 鐃緒申直鐃渋わ申(鐃獣件申鐃夙わ申鐃緒申)同鐃緒申鐃祝なり、鐃緒申鐃曙ぞ鐃緒申鐃銃縁申鐃緒申鐃粛㍼申鐃緒申屬鐃� ${\mathbb{C}}[G]$ 鐃緒申鐃緒申鐃叔ワ申鐃緒申砲覆襦�

命鐃緒申 10.1 $Z({\mathbb{C}}[G])$ 鐃熟種申鐃塾よう鐃淑器申

鐃緒申有鐃渋個わ申(鐃縦とわ申鐃銃わ申)直鐃術わ申分鐃薯する。

$Z(R_i)={\mathbb{C}}$
-鐃獣件申鐃叔￥申 ${\mathbb{C}}$ 鐃緒申有鐃渋種申鐃緒申鐃塾わ申里鐃宿�申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔わ申鐃暑。

鐃縦わ申鐃叔に￥申鐃緒申鐃緒申聞澆暴鐃緒申廚砲覆鐃� $M_n({\mathbb{C}})$ 鐃塾削申鐃緒申鐃叔ワ申鐃緒申鐃緒申鐃緒申鵑欧討鐃緒申鐃緒申鐃緒申鐃�

鐃緒申 鐃緒申鐃縮に￥申鐃緒申

鐃塾醐申

鐃祝わ申鐃緒申鐃緒申鐃銃￥申

鐃緒申

鐃塾削申鐃緒申鐃叔ワ申鐃緒申砲覆襦� 鐃夙わ申鐃祝￥申 $M_n({\mathbb{C}})$ 鐃塾醐申 $x_l=E_{11}+E_{22}+\dots+ E_{ll}$ ( $E_{ij}$ 鐃緒申鐃緒申鐃旬刻申鐃緒申) 鐃祝わ申鐃緒申鐃緒申鐃銃￥申 $J_l=M_n({\mathbb{C}}) x_l$ 鐃緒申 $M_n({\mathbb{C}})$ 鐃塾ワ申鐃叔ワ申鐃緒申任鐃緒申襦�

$\displaystyle J_1 \subset J_2 \subset J_3\subset J_4\subset \dots \subset J_n=M_n({\mathbb{C}}).$

鐃緒申鐃緒申 10.1 鐃縮随申

鐃緒申鐃緒申鐃緒申鐃塾件申 $\mathbb{D}_8$ 鐃塾件申鐃緒申 ${\mathbb{C}}[\mathbb{D}_8]$ 鐃緒申鐃緒申聴幣鐃塾環わ申直鐃術わ申分鐃薯せよ。