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Math Help - Ideals of Algebraic Sets

  1. #1
    Senior Member slevvio's Avatar
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    Ideals of Algebraic Sets

    Hello, I was wondering if someone could give me a hint about where to start with the following problem. Any help would be appreciated.

    (definitions)
    Let k be an algebraically closed field. Then let J,J' \subseteq k[x_1,\ldots,x_n] be ideals. Then let X = V(J), X' = V(J'), i.e. algebraic sets. The ideal of X is  I_X := \{ f \in k[x_1 ,\ldots, x_n] | f(x) = 0 \forall x \in X\}.

    (problem)
    give an example to show that I_{X \cap X'} \not= I_X + I_{X'}
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  2. #2
    MHF Contributor

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    Re: Ideals of Algebraic Sets

    Quote Originally Posted by slevvio View Post
    Hello, I was wondering if someone could give me a hint about where to start with the following problem. Any help would be appreciated.

    (definitions)
    Let k be an algebraically closed field. Then let J,J' \subseteq k[x_1,\ldots,x_n] be ideals. Then let X = V(J), X' = V(J'), i.e. algebraic sets. The ideal of X is  I_X := \{ f \in k[x_1 ,\ldots, x_n] | f(x) = 0 \forall x \in X\}.

    (problem)
    give an example to show that I_{X \cap X'} \not= I_X + I_{X'}
    this is just the geometric version of this question, that i've already answered.
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