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Math Help - Elaboration on Correspondence Theorem Result

  1. #1
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    Elaboration on Correspondence Theorem Result

    Can someone explain why \mathbb{Z}[x]/(x^2+3,5) \cong \mathbb{F}_{25}
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Elaboration on Correspondence Theorem Result

     Z[x] \to Z_{5}[x] by f(x)  \in Z[x] = a_nx^n + ... + a_0 \to (a_n) mod 5 x^n +... + (a_0) mod 5 . is a homomorphism.
    Then Z[x]/<x^2+3,5> \to Z_{5}[x]/<x^2+3> since x^2 + 3 is irreducible in Z_{5}[x] (no zeros are there). Z_{5}[x]/<x^2+3> is a field containing 5^2 elements.
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