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Math Help - Maximal ideal

  1. #1
    Junior Member
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    Maximal ideal

    Hi,

    I've following homomorphism: h:\mathbb{Z}[X] \rightarrow \mathbb{Z}, h(w)=w(0), where w is a polynomial.
    \mathbox{ker}h - prime ideal but not maximal.

    How can I find all maximal ideals?

    Thanks for help.
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  2. #2
    Senior Member roninpro's Avatar
    Joined
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    You can start by noting that M is maximal in your ring if and only if \mathbb{Z}[X]/M is a field.
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