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Math Help - Nilpotents

  1. #1
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    Nilpotents

    Letting R be a commutative ring, and letting I = {a in R | a^n =0 for some n in S} where S is the set of positive integers.
    Prove I is an ideal of R.
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  2. #2
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    Quote Originally Posted by Coda202 View Post
    Letting R be a commutative ring, and letting I = {a in R | a^n =0 for some n in S} where S is the set of positive integers.
    Prove I is an ideal of R.
    This is just saying that the nilradical is an ideal.

    note if x^n=0 then \forall a \in R (ax)^n=0

    Also if x^n=y^n=0 then

     (x+y)^{m+n-1}= \sum_{k=0}^{m+n-1}{n \choose k} x^{m+n-1-k}y^k=0.
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