Since 2Z is a maximal ideal of Z, 2Z[X] is an ideal of Z[X] but it is not maximal since Z[X]/2Z[X]~(Z/2Z)[X] is not a field.(adsbygoogle = window.adsbygoogle || []).push({});

I'm wondering if a is a maximal ideal of A, when can you say that a[X] is a maximal ideal of A[X]?

I suppose that for any A which does not have the zero ideal as a maximal ideal, the polynomial X would not be a unit in (A/a)[X]. So... a[X] is a maximal ideal of A[X] if and only if a=0 is maximal in A?

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# Maximal ideals in Z[X]

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