Let f(x)=x^4-4. a) Determine the degree of the splitting field K of f(x) over Q. b) Determine all the sub extensions F such that Q is contained in F and F is contained in K, and arrange these in a graph ordered by inclusion.

Let f(x)=x^4-4. a) Determine the degree of the splitting field K of f(x) over Q. b) Determine all the sub extensions F such that Q is contained in F and F is contained in K, and arrange these in a graph ordered by inclusion.

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 16E: Each of the polynomials in Exercises is irreducible over the given field . Find all zeros of in...

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