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    Basis and Finite and Infinite Field Extensions

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    Find a basis for the extension of and also calculate
    We know already that is infinite.
    Give an example of fields and (with neither nor equal to ) such that:
    a) and are both infinite
    b) is infinite and is finite.

    (See attached file for full problem description with proper symbols)

    All gaps are Q, the rational numbers.

    © BrainMass Inc. brainmass.com December 15, 2022, 5:04 pm ad1c9bdddf
    https://brainmass.com/math/finite-element-method/basis-finite-infinite-field-extensions-58988

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    1. Find a basis of the extension of and also calculate
    Let , then , ...

    Solution Summary

    Basis and Finite and Infinite Field Extensions are investigated. The solution is detailed and well presented.

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