Let F be a field of characteristic 0, and let E be the splitting field of some f(x) E F[x] such that Gal(E/F) - D5. Prove that E has a subfield K containing F with K 6= E, F such that K is the splitting field of some f(x) E F[x]. What is [K :F]?

Let F be a field of characteristic 0, and let E be the splitting field of some f(x) E F[x] such that Gal(E/F) - D5. Prove that E has a subfield K containing F with K 6= E, F such that K is the splitting field of some f(x) E F[x]. What is [K :F]?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 16E

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Let F be a field of characteristic 0, and let E
be the splitting field of some f(x) E F[x] such
that Gal(E/F) - D5. Prove that E has a subfield
K containing F with K 6= E, F such that K is the
splitting field of some f(x) E F[x]. What is [K
:F]?

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