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    Splitting Fields

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    Let E be an extension of F and f(x) be in F[x]. Also, let Φ be an automorphism of E leaving every element of F fixed. Prove that Φ must take a root of f(x) lying in E into a root of f(x) in E.

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    © BrainMass Inc. brainmass.com October 9, 2019, 7:22 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/splitting-fields-116040

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    Let E be an extension of F and f(x) be in F[x]. Also, let Φ be ...

    Solution Summary

    Splitting fields are investigated. The solution is detailed and well presented.

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