Exercise 4, § 9

Let K be a field. Show that there exists a smallest subfield F of K and that F is canonically isomorphic either to the field $\mathbf{Q}$ or to the field $\mathbf{Z}/p\mathbf{Z}$ for some prime number $p$. In the first case (resp. second case) K is said to be of characteristic 0 (resp. $p$).