鐃緒申鐃緒申鐃� II 鐃緒申鐃緒申 No.13

鐃緒申鐃緒申 13.1 $A=\mbox{${\Bbb R}$ }[X,Y,Z]$ 鐃塾ワ申鐃叔ワ申鐃緒申

鐃祝つわ申鐃銃￥申鐃緒申鐃緒申鐃巡い鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申

1.

鐃塾鰹申鐃緒申鐃緒申颪④覆鐃緒申鐃緒申鐃�

2.

鐃緒申

鐃叔なわ申鐃緒申

鐃叔￥申

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申鐃夙わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申

鐃塾醐申鐃叔￥申

鐃緒申

鐃叔のワ申鐃初ス鐃緒申表鐃緒申鐃緒申里箸鐃緒申襦�

3.

鐃緒申鐃�

鐃祝つわ申鐃銃￥申

$\begin{displaymath}fg=a(X,Y,Z) (X^2+Y^2-Z^2)+b(X,Y,Z)((1+X^2+Y^2-Z^2)X-Y) \end{displaymath}$

鐃緒申澆鐃緒申鐃緒申茲�申鐃� $a,b \in A$ 鐃緒申尊櫃傍鐃緒申覆鐃緒申鐃緒申鐃�

4.

鐃塾醐申

鐃緒申

鐃緒申鐃緒申鐃塾種申

鐃塾ワ申鐃初ス鐃夙わ申鐃緒申表鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃縦まり、

$\begin{displaymath}[Z^4+3Z^2]=[p(X)] \end{displaymath}$

鐃夙なわ申

鐃緒申鐃縦居申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 13.2 $\phi: \mbox{${\Bbb R}$ }[X,Y,Z]\to \mbox{${\Bbb R}$ }[T]$ 鐃緒申

$\begin{displaymath}\phi(X)=T, \quad \phi(Y)=T^2, \quad \phi(Z)=T^3 \end{displaymath}$

鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申里箸鐃緒申鐃�

1.: $\ker(\phi)$ 鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�
2.: $\operatorname{Image}({}^a\phi)$ 鐃塾鰹申鐃緒申鐃緒申颪④覆鐃緒申鐃緒申鐃�
3.: ${}^a\phi(0)$ , ${}^a\phi(-1)$ , ${}^a\phi(1)$ , ${}^a\phi(2)$ 鐃薯それぞ鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�