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Unformatted text preview: A is a normal lower triangular matrix over the complex numbers, the A is a diagonal matrix. 6. Let R = Z [ X ] and let I = (2 ,X ). Prove that I is not a free R-module but it is torsion free. 7. Let F be a nite eld. Prove that the product of the non zero elements of F is-1. 8. Let = p 2 + 2. Find the minimal polynomial of over Q and show that = p 2- 2 is another root of this minimal polynomial. Show that the degree of Q ( ) over Q is 4. Prove that sending to = p 2- 2 is an automorphism of Q ( ) over Q . Describe the Galois group of Q ( ) over Q . 1...
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- Spring '11