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Algebraic Geometry Question - on ideals of algebraic sets

  1. Oct 9, 2011 #1
    Hello everyone, I was wondering if I could get some advice for the following problem:

    I have two algebraic sets X, X', i.e. X = V(J), Y = V(J'), and let I(X),I(Y) be the ideals of these sets, i.e. I(X) ={x [itex]\in[/itex] X | f(x) = 0 for all x [itex]\in X[/itex]}. I am trying to show that I(X [itex]\cap[/itex] Y) is not always equal to I(X) + I(Y), so I have tried many examples of ideals of [itex]\mathbb{C}[X][/itex] but I am not getting anywhere.

    Any help would be appreciated!

    Thanks
     
  2. jcsd
  3. Oct 9, 2011 #2

    mathwonk

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    look in C[X,Y], and try a couple of sets that meet tangentially.
     
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