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Math Help - Polynomial Rings over fields with characteristic p

  1. #1
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    Polynomial Rings over fields with characteristic p

    Let char(\mathbb{F}) = p, where \mathbb{F} is a field. For what fields is \frac{\mathbb{F}}{<x^2+7x+7>} an integral domain?

    I tried using the Frobenius homomorphism, but I kept going in circles. Any ideas on how to proceed? (and please no direct Galois theory, if possible, as I don't know any)
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  2. #2
    Junior Member sorv1986's Avatar
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    Re: Polynomial Rings over fields with characteristic p

    F should be a field over which the polynomial is irreducible.
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