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Math Help - ring homomorphism

  1. #1
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    ring homomorphism

    phi:Q[t] -> R be defined phi(t)=rt(2) and with elements of Q mapping themselves in R. Prove that rt(8) is in Im(phi)

    let h=(t^4)+(t^4)-4 show phi(h)=0

    Q is rationals, R is reals.

    ok i can define Im(phi) and then i say rt(8)=phi*rt(2) => phi=2..im really lost help need help pretty quick, exam revision!
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by benjyboy View Post
    phi:Q[t] -> R be defined phi(t)=rt(2) and with elements of Q mapping themselves in R. Prove that rt(8) is in Im(phi)

    let h=(t^4)+(t^4)-4 show phi(h)=0

    Q is rationals, R is reals.

    ok i can define Im(phi) and then i say rt(8)=phi*rt(2) => phi=2..im really lost help need help pretty quick, exam revision!
    Part one is actually quite simple - you just have to remember that \sqrt{a^n} = (\sqrt{a})^n.

    For part two you meerly substitute in \sqrt{2} for t as \phi is a ring homomorphism (a ring homomorphism is a mapping from a ring to another ring such that (ab+c)\phi = (a\phi)(b\phi)+c).

    I hope that helps?

    Also, this would have been more suited to the "Abstract Algebra" forum as it is, well, abstract algebra...
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