: ����ʸ��ˤĤ���...
����ر齬 I ���� No.9
�����ִġפȤ�����ñ�̸�����IJĴ��ĤǤ���Ȥ����ִĤν�Ʊ���פ�
ñ�̸����ݤĤ�Τ�����ͤ��뤳�Ȥˤ��ޤ���
��� 9.1
����

�����ʬ���(unique factorization domain:UFD) �Ǥ���Ȥϡ�

��Ǥ�դθ�

���Ǹ����Ѥ�

$p_1,...,p_k$ �� $R$ ���Ǹ�
�Τ褦�˽񤱤�Ȥ��˸����ޤ���
(

����ˤ�Ʊ����Τ����äƤ�褤��)
��� 9.2
����

�� ñ�।�ǥ������� (principal ideal domain:PID) �Ǥ���Ȥϡ�

�Τ��٤ƤΥ��ǥ��뤬ñ�।�ǥ���(��Ĥθ�����������륤�ǥ���)�Ǥ���Ȥ��˸����ޤ���
���줫��ä��δ� (3�󤰤餤)��Σ��ĤΥ����פδĤ�����ˤʤ�ޤ�������Ū�ˤϡ�
ED

PID

UFD
�Ȥ������¤ȡ����㡢���������ΰ�̣��ʬ��褦�ˤʤ�� OK �Ǥ���
�ޤ���˾夲������Τ����δ��Ĥ����Ѹ�˴ؤ������꤫��Ϥ�ޤ���
���� 9.1 (���󽸹������γ�ǧ)

��桼����å�����Ȥ���

�����
9.3 �˽ФƤ�������Ȥ��ޤ������λ���Ǥ�դ�

����ʬ����

���Ф��ơ�

����ǽŤ����Ǿ��Τ��(�ְ��ַڤ���Ρ�)�����뤳�Ȥ򼨤��ʤ�����
��
�����󽸹�Ǥ���פȤϡ���
��Ǥ�դ���ʬ����
�ϺǾ�������ġפȤ������ȤǤ����������ǡ���
�θ��νŤ��ν����
��
�Ȥ��ƺ��Ѥ���ȡ�������˺Ǿ���������Ȧ�Ǥ��������
�Ȥ���С�
�������ΤȤ������Ȥˤʤ�ޤ���(���ա����ַڤ����ϰ�ĤȤϸ¤�ޤ���)
���� 9.2
�桼����å������ñ�।�ǥ�������Ǥ��뤳�Ȥ򼨤��ʤ�����(�ҥ�ȡ�

��桼����å�����Ȥ���

�򤽤Υ��ǥ���ΰ�ĤȤ��ޤ���

�ʤ�ñ�� (0 �����������)�ΤǤ褤��

�ʤ顢

�θ��Τ��������ַڤ�����ȤäƤߤʤ�����)
���� 9.3

�ϥ桼����å�����Ǥ��뤳�Ȥ�����˱�äƼ����ʤ�����

���� 9.4
��

��ΰ��ѿ�¿�༰��
![$ K[X]$](img35.png)
�ϥ桼����å�����Ǥ��뤳�Ȥ�����˱�äƼ����ʤ�����
���� 9.5

(���λ��躬�ΰ��)�Ȥ���Ȥ���

![$ [\omega]$](img38.png)
���ΤǤ��뤳�Ȥ򼨤��ʤ�����
���� 9.6
![% latex2html id marker 1102
$ {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}]$](img39.png)
�ϡֽŤߴؿ���

��
��������뤳�Ȥˤ�ꡢ�桼����åɴĤȤʤ뤳�Ȥ򼨤��ʤ�����(�ҥ�ȡ�
![% latex2html id marker 1114
$ \alpha,\beta \in {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}], \beta \neq 0$](img48.png)
�Ȥ���Ȥ���

��

�dz�ä��������ˤϡ�

��
![% latex2html id marker 1122
$ {\mbox{${\mathbb{Z}}$}}[\sqrt{-1}]$](img52.png)
�θ��Ƕ�����Ƥߤʤ�����)
���� 9.8

(

�λ��躬�ΰ��) �Ȥ��ޤ������ΤȤ���
![$ {\mbox{${\mathbb{Z}}$}}[\omega]$](img65.png)
�ϥ桼����åɴĤǤ��뤳�Ȥ򼨤��ʤ�����
: ����ʸ��ˤĤ���...
ʿ��17ǯ12��13��