what is the characteristic of field
Answers
Explanation:
An invariant of a field which is either a prime number or the number zero, uniquely determined for a given field in the following way. If for some n>0
0= ne= e+e+e+.........+e
where e is the unit element of the field F, then the smallest such n is a prime number; it is called the characteristic of F. If there are no such numbers n, then one says that the characteristic of F is zero or that F is a field of characteristic zero. Sometimes such a field is said to be without characteristic or of characteristic infinity (∞). Every field of characteristic zero contains a subfield isomorphic to the field of all rational numbers, and a field of finite characteristic p contains a subfield isomorphic to the field of residue classes modulo p: in each case this is the prime field.