On The Of Nilpotent Elements Of Zn As A Ring And Zd As A Module Over Zn

In this paper, we investigate the possible relationship between the nilpotent elements of ℤn as  ring  and Zd  as a modular Zn.  we provide example of the  fact that a nilpotent  element in zn may not be nilpotent in the Zn  - module zd even if d=n. We give a condition under which a nipotent element  in zn beomes  a  nilpotent element in the Zn module  Zd . We  also obtain a partial converse of the above fact for the special case d = n and  a certain condition.