An element a of a commutative ring R is called nilpotent if for some nN.

Find the nilpotent elements inZ6,Z12,Z8, andZ36

Then show that the collection N of all nilpotent elements in R is an ideal.

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- Jul 22nd 2010, 05:51 PMmeggnogNilpotent Element of a Ring
An element a of a commutative ring R is called nilpotent if for some n

**N**.

Find the nilpotent elements in**Z**6,**Z**12,**Z**8, and**Z**36

Then show that the collection N of all nilpotent elements in R is an ideal. - Jul 23rd 2010, 02:15 PMJose27
For the first one, note that we have a non-zero nilpotent in 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.