4. [5 marks] Let F be a field and F is a fixed algebric closure of...

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4. [5 marks] Let F be a field and F is a fixed algebric closure of F. Suppose E < F is an arbitrary extension field of F and K is a finite Galois extension of F (called "normal extension" in the textbook). (a) Show that the joint K VE is a finite Galois extension over E. (b) Show that the restriction map Gal(KVE/E) Gal(K/EnF) defined by ok is an isomorphism. 4. [5 marks] Let F be a field and F is a fixed algebric closure of F. Suppose E < F is an arbitrary extension field of F and K is a finite Galois extension of F (called "normal extension" in the textbook). (a) Show that the joint K VE is a finite Galois extension over E. (b) Show that the restriction map Gal(KVE/E) Gal(K/EnF) defined by ok is an isomorphism.