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Math Help - Nilpotent Element of a Ring

  1. #1
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    Nilpotent Element of a Ring

    An element a of a commutative ring R is called nilpotent if a^n=0 for some n \epsilon N.

    Find the nilpotent elements in Z6, Z12, Z8, and Z36

    Then show that the collection N of all nilpotent elements in R is an ideal.
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  2. #2
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    For the first one, note that we have a non-zero nilpotent in \mathbb{Z} _n iff the prime factorization of n exhibits at least one prime to a power distinct from 1. Can you then guess what elements are these nilpotents?

    For the second use the binomial theorem.
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