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Math Help - Radical ideal

  1. #1
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    Radical ideal

    Let I=<f_1,f_2> \subset \mathbb{C}[x,y] be an ideal generated by a linear and an irreducible quadratic polynomial.

    Suppose that g\in \sqrt{I}. Show that g^2\in I
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  2. #2
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    Quote Originally Posted by KaKa View Post
    Let I=<f_1,f_2> \subset \mathbb{C}[x,y] be an ideal generated by a linear and an irreducible quadratic polynomial.

    Suppose that g\in \sqrt{I}. Show that g^2\in I
    Is it not true that the definition of \sqrt{I} is \{ h | h^2 \in I \}?
    Thus, what you are asking is simply a definition.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Is it not true that the definition of \sqrt{I} is \{ h | h^2 \in I \}?
    no. the definition is: \sqrt{I}=\{h | \ \exists n \in \mathbb{N}: \ h^n \in I \}. i don't like this problem very much, but i might think about it.
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