1. Let K = Q(V5+ V5).%3D(a) What is the minimal polynomial of V5+ V5 over Q? Justify your answer.(b) Find all extensions of fields QCLCK and justify your answer.(c) Show that the extension QCK is a Galois extension. What is Aut(K|Q)?

It is given that, K = ℚ5+5. Then we have to answer the following questions : (a) What is the…

Answered: 1. Let K = Q(√5 + √5). (a) What is the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 7E

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1. Let K = Q(√5 + √5). (a) What is the minimal polynomial of √5+ √5 over Q? Justify your answer. (b) Find all extensions of fields QCLCK and justify your answer. (c) Show that the extension QC K is a Galois extension. What is Aut(K|Q)?