Let p be prime, m be a positive integer.

1-show that each element c of Z(p^m) is either a unit or is nilpotent.

I know nilpotent is when there is a pos. int. k so that c^k=0, and that a unit is such that c*k=1, but I don't know how to show this.

2- How many units are in Z(p^m)? nonunits? Explain.