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Math Help - Elementary Algebraic Geometry - D&F Section 15.1 - Exercise 15

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    Elementary Algebraic Geometry - D&F Section 15.1 - Exercise 15

    Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows:

    ----------------------------------------------------------------------------------------------------

    If   k = \mathbb{F}_2  and   V = \{ (0,0), (1,1) \} \subset \mathbb{A}^2 ,

    show that  \mathcal{I} (V) is the product ideal  m_1m_2

    where  m_1 = (x,y)  and  m_2 = (x -1, y-1) .

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    I am having trouble getting started on this problem.

    One issue/problem I have is - what is the exact nature of  m_1, m_2 and   m_1m_2 . What (explicitly) are the nature of the elements of these ideals.

    I would appreciate some help and guidance.

    Peter



    Note: D&F define  \mathcal{I} (V)  as follows:

      \mathcal{I} (V) = \{ f \in k(x_1, x-2, ......... , x_n) \ | \ f(a_1, a_2, ......... , a_n) = 0 for all   (a_1, a_2, ......... , a_n) \in V \}
    Last edited by Bernhard; October 30th 2013 at 04:55 PM.
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