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Math Help - Isomorphic rings in Q[x]

  1. #1
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    Isomorphic rings in Q[x]

    Prove \frac{\mathbb{Q}[x]}{<x^2+4x+2>} \cong \frac{\mathbb{Q}[x]}{<x^2-2>} . It's obvious that \frac{\mathbb{Q}[x]}{<x^2-2>} \cong \mathbb{Q}[\sqrt{2}] but I can't get the other way, and it seems to be a logical way to prove this.
    Any help is appreciated.
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  2. #2
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    Re: Isomorphic rings in Q[x]

    well, it should also be obvious that \frac{\mathbb{Q}[x]}{\langle x^2+4x+2 \rangle} \cong \mathbb{Q}[\sqrt{2} - 2] = \mathbb{Q}[\sqrt{2}].
    Thanks from wsldam
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