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Math Help - Quotient ring / field

  1. #1
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    Quotient ring / field

    How do I prove that the quotient ring Z[x]/(f,2) where f=x^3+2x^2+x+1 is actually a field? [(f,2) is an non-principal ideal)
    Thanks!
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  2. #2
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    Quote Originally Posted by merus View Post
    How do I prove that the quotient ring Z[x]/(f,2) where f=x^3+2x^2+x+1 is actually a field? [(f,2) is an non-principal ideal)
    Thanks!
    Hint: The maximal ideal of Z[x] has the form (f(x), p) where p is a prime number and f(x) is a polynomial in Z[x] which is irreducible modulo p (here).
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  3. #3
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    Wow, thank you very much!
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