Answer to Question #70740 in Abstract Algebra for Pkm

Question

The characteristic of a finite field is zero. Is this statement true or false, justify your answer.

Answer 1

F is a field.
The statement is false because the characteristic of a finite field is the prime number p>0 and the number of elements in F is q=p^n. If p=0 and a<>e, a є F, it is true for a finite field that a^q=a, but a^0=e is a contradiction.