You can prove that , so its characteristic is and its prime field is .
for each element we have:
so, the characteristic of this field is and its prime field is .
the task is to define characteristics and prime fields of following fields:
The seems to be following kind of field:
So, the 's order is , but I don't understand, what is it's characteristic. Prime field should be something like:
I think the second one is: .
But I have no idea, what it's characteristic or prime field could be.
The third one is completely mysterious to me - I don't understand it's structure at all.
Any help is appreciated. Thanks very much in advance!