The sum of a nilpotent left ideal and a nil left ideal

[frankusho]

1. Show that the sum of a nilpotent left ideal and a nil left ideal is a nil left ideal.





2. The attempt at a solution

So far, I have no idea where to begin.

 

[Mark44]

Definitions?

 

[frankusho]

A left deal I of a ring R is left nilpotent if there is a positive integer n > 0 such that Iⁿ=0



A nil left ideal is a left ideal in which every element is nilpotent, i.e. for all i in I there exists a n>0such that iⁿ=0

 

[Mark44]

So take an arbitrary element from a nilpotent left ideal and an arbitrary element from a nil left ideal and add them. What do you get? What should you get?