Let f(x) = X3+2 and N = {a C|f(a) = 0} and L = Q(N). (a)...

 

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Let f(x) = X3+2 and N = {a C|f(a) = 0} and L = Q(N). (a) Write the elements of 2. (b) Find the degree |L: Q|. (c) Is L/Q a Galois extension? (d) Determine the Galois group Gal(L/Q). Let f(x) = X3+2 and N = {a C|f(a) = 0} and L = Q(N). (a) Write the elements of 2. (b) Find the degree |L: Q|. (c) Is L/Q a Galois extension? (d) Determine the Galois group Gal(L/Q).