Exercise 1, § 4

Let K be a field and $(E_i)_{i \in I}$ any family of extensions of K. Show that there exists an extension E of K and for each $i \in I$, a K-isomorphism $u_i$ of $E_i$ into E such that E is generated by the union of the $u_i(E_i)$ (argue as in Prop. 4 (V, p. 22)).