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Math Help - how to prove

  1. #1
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    how to prove

    How to prove that the fields F2[x]/ (x^4+x+1) and F2[x]/ (x^4+x^3+x^2+x+1) are isomorphic. can any one explain it to me .
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint :

    Denote:

    I=(x^4+x+1)

    then,

    \mathbb{F}_2[x]/ I=\left\{{a_3x^3+a_2x^2+a_1x+a_0+I:a_i\in \mathbb{F}_2}\right\}

    Idem for J=(x^4+x^3+x^2+x+1) .


    Fernando Revilla
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