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Math Help - Help algebraic integer!

  1. #1
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    Help algebraic integer!

    Let a be an algebraic integer and suppose that f(a)=0, where f(x) in Q[x] is irreducible and monic. Show that f(x) in Z[x]. Please help me, thanks so much!
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by thanhuthe View Post
    Let a be an algebraic integer and suppose that f(a)=0, where f(x) in Q[x] is irreducible and monic. Show that f(x) in Z[x]. Please help me, thanks so much!
    What have you done so far? The key point is really that a is the root of some monic polynomial, g(x), with coefficients in Z. You need to show that f(x)=g(x).
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