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Thread: Isomorphism of fields

  1. #1
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    Isomorphism of fields

    hi! I have problems with demostration

    Show that there is an isomorphism of fields:

    \mathbb{R} \left [ x \right ] / (x^2+1)  \cong   \mathbb{R} \left [ x \right ]  / (x^2+x+1)

    Hint: Both are isomorphic to \mathbb{C}

    I do not know how to use the hint

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  2. #2
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    Re: Isomorphism of fields

    Find an isomorphism between $\mathbb{R}[x]/(x^2+1) $ And $\mathbb{C} $. Do the same for the second field. Then compose the two isomorphisms to generate an isomorphism between the two.
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  3. #3
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    Re: Isomorphism of fields

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