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Math Help - Subring of the complex

  1. #1
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    Subring of the complex

    Let A the subring of the complex A=\{ a + b \sqrt{2}: a,b \in \mathbb{Z}\}

    a) Prove that A is a \mathbb{Z}-module and an A-module, with the product as action

    b) Prove that the function a + b \sqrt{2} \rightarrow a+b is a homomorphism of \mathbb{Z}-modules from A to A but isnīt a homomorphism of A-modules

    c) Prove that, as \mathbb{Z}-module, A is isomorphic to \mathbb{Z} \oplus \mathbb{Z}

    thanks!!
    Last edited by roporte; November 7th 2008 at 09:29 PM. Reason: mistake
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