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Math Help - Sum and Intersection

  1. #1
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    Sum and Intersection

    I have the ring Z and two ideals I and J of Z. I need to find for every two ideals of the ring Z their sum and intersection.

    What exactly does this mean? Can someone show me a possible solution?
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  2. #2
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    Quote Originally Posted by KevinKH View Post
    I have the ring Z and two ideals I and J of Z. I need to find for every two ideals of the ring Z their sum and intersection.

    What exactly does this mean? Can someone show me a possible solution?
    The intersection of I,J is I\cap J another ideal of \mathbb{Z}. (Remember they are sets).

    I never heard anything about being able to "add" two ideals together. Unless you want to find,
    \{i+j|i\in I \mbox{ and }j\in J\}.
    That is not necessarily an ideal because it not necessarily has the form,
    n\mathbb{Z}.
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    What do you think I should write as a solution for that question? It seems to just ask for the definition, but it was given in a problem above. Any suggestions?
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    Quote Originally Posted by KevinKH View Post
    What do you think I should write as a solution for that question? It seems to just ask for the definition, but it was given in a problem above. Any suggestions?
    Are you saying yout book in the problems section asks you to define a natural meaning for "sum of two ideal"? If so then use what I said above, the set formed from all possible additions of the elements.
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