How can I show that every finite field F has a characteristic of the field using its definition?
Thank you for any help.
I am sure you are familar with the rule that all we need to do is check whether,
for some positive integer to show there exists a charachteristic.
Now, the additive group of the field is a finite group because the field is finite. Thus, has finite order. Thus, where is the identity element in . Thus, it must have a non-zero charachteristic.