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Math Help - a maximal ideal

  1. #1
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    a maximal ideal

    Prove that the ideal (x) in Q[x] is maximal. (Q[x] is the set of all polynomials with rational coefficients
    any help would be appreciated
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    It is easy to prove that

    \mathbb{Q}[x]/(x)=\{\lambda+(x):\;\lambda\in \mathbb{Q}\}

    As a consequence,

    \mathbb{Q}[x]/(x) is a field.

    Fernando Revilla
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