(a) For any u 1 , . . . , u n F and any permutation...

(a) For any u₁, . . . , u_n ϵ F and any permutation σ ϵ S_n, K(u₁, . . . , U_n) = K(u_σ(1),. .. , u_σ(n))

(b) K(u₁, ... , U_n-1)(un) = K(u₁, ... , U_n). 

(c) State and prove the analogues of (a) and (b) for K[u₁, ... , U_n].

(d) If each u_i is algebraic over K, then K(u₁, ... , U_n) = K[u₁, ... , u_n].