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Math Help - Rings and Integral Domains

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    Super Member Aryth's Avatar
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    Rings and Integral Domains

    Let \mathcal{Z}[x] be the set of all polynomials in the variable x, with coefficients from \mathcal{Z} and the usual operations of addition and multiplication.

    Let S be the set of polynomials in \mathcal{Z}[x] with roots at x=0 and x=1. Prove that S is a subring of \mathcal{Z}[x].
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    Quote Originally Posted by Aryth View Post
    Let \mathcal{Z}[x] be the set of all polynomials in the variable x, with coefficients from \mathcal{Z} and the usual operations of addition and multiplication.

    Let S be the set of polynomials in \mathcal{Z}[x] with roots at x=0 and x=1. Prove that S is a subring of \mathcal{Z}[x].
    Do it by definition.
    For example, for additive closure say f(x),g(x) \in S.
    Then f(x)+g(x) \in S since f(0)+g(0) = 0 + 0 = 0 and f(1)+g(1) = 0 + 0 = 0.
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