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Ring Ideals

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that the intersection of any set of ideals of a ring is an ideal.

    2. Relevant equations
    A nonempty subset A of a ring R is an ideal of R if:
    1. a - b ε A whenever a, b ε A
    2. ra and ar are in A whenever a ε A and r ε R

    3. The attempt at a solution
    My guess is that i need to start with a collection of ideals,
    write a representation of the form of the intersection of those ideals,
    upon which i can take two generic elements and apply the ideal test above

    Putting this into symbols seems to be the tricky part for me.
  2. jcsd
  3. Nov 23, 2008 #2


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    Science Advisor
    Homework Helper

    You don't need a representation of the form of the intersection. Just apply the definition directly. For example, to apply 1, take a & b in the intersection. What can you say about a-b?
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