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Math Help - Galois

  1. #1
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    Galois

    Hi
    Let \alpha{=2^1/3}, \omega {=e^2\pi {i/3)}}

    how can we show Q(\alpha ,\omega } is a the splitting field of t^3-2

    Thank you
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  2. #2
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    May 2010
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    Quote Originally Posted by jerad View Post
    Hi
    Let \alpha{=2^1/3}, \omega {=e^2\pi {i/3)}}

    how can we show Q(\alpha ,\omega } is a the splitting field of t^3-2

    Thank you
    Just check t^3-2 \in Q[t] splits in Q(\alpha ,\omega) and verify that all the roots of t^3-2 \in Q[t] belong to Q(\alpha ,\omega). Make sure that t^3-2 \in Q[t] does not factor completely into linear factors in any proper subfield of Q(\alpha ,\omega) containing Q.
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