It is a fact, which we can verify by cubing, that the zeros of x'- 2 in Q are -1+iv3 aj = V2, az = 21-iv3 a2 = and 2 where 2, as usual, is the real cube root of 2. Use this information in Exercises 4 through 4. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2) onto a subfield of Q. 5. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2, /3) onto a subfield of Q. 6. Describe all extensions of the automorphism 3-v3 of Q(/3) to an isomorphism mapping Q(i, 3, V2) onto a subfield of O.

It is a fact, which we can verify by cubing, that the zeros of x'- 2 in Q are -1+iv3 aj = V2, az = 21-iv3 a2 = and 2 where 2, as usual, is the real cube root of 2. Use this information in Exercises 4 through 4. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2) onto a subfield of Q. 5. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2, /3) onto a subfield of Q. 6. Describe all extensions of the automorphism 3-v3 of Q(/3) to an isomorphism mapping Q(i, 3, V2) onto a subfield of O.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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