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Math Help - Radical of an ideal

  1. #1
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    Radical of an ideal

    Let I an ideal of a conmutative ring A. We define the radical of I

    \sqrt{I}=\{ x \in A | \exists n such.that. x^n \in I \}

    A) Prove that the radical of I is an ideal
    B) Describe the radical of some ideal of \mathbb{Z}
    C) If A=K[X_1, \dots, X_n] prove that \sqrt{I}\subset \mathcal{I}(\mathcal{V}(I))
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