Prime filed

1. Jul 18, 2011

arthurhenry

Why is it not possible for a filed to have have two prime fileds one isomorphic to Zp and the other isomorphic to Zq for p and q primes.
Thank you

2. Jul 19, 2011

SteveL27

There's only one characteristic. 1 + 1 + ... + 1 = 0 for some prime number p of 1's (where 1 is the multiplicative identity of the field) and p is therefore the characteristic, and Z/pZ is the prime field.