Exercise
How may ideals does Z/2Z × Z/2Z have?
0
1
2
3
4
No. The singleton {(0,0)} is always an ideal.
No. The singleton {(0,0)} and the whole set Z/2Z × Z/2Z are always ideals.
Wrong. Besides the singleton {(0,0)} and the whole set Z/2Z × Z/2Z,
we have the ideal {(0,0),(1,0)}.
Wrong.
Besides the singleton {(0,0)} and the whole set Z/2Z ×
Z/2Z,
we have the ideals {(0,0),(1,0)} and {(0,0),(0,1)}.
Correct.