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Homework Help: Nil radical proof

  1. Dec 7, 2006 #1
    1. The problem statement, all variables and given/known data
    Let A be any ideal of a commutative ring with unity R. Show that the nil radical of A, N(A)= {r|r^n is in A} where n is a positive integer, and n depends on r.

    2. Relevant equations

    3. The attempt at a solution

    i dont quite understand the concept of the nil radical of A, what would be an element of this ideal? the unity element is in for every n a positive integer, so it's non empty but i'm still a little confused.
  2. jcsd
  3. Dec 7, 2006 #2


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    Homework Helper

    Is the equation you have a definition, or something you're asked to prove? If it's a definition, then what are you being asked to prove? If you're being asked to prove that equation, then what's the definition of N(A)?
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