Referring to Exercise 30, show that if N is the nilradical of a commutative ring R, then R/N has as nilradical the trivial ideal {0 + N}.

Data from Exercise 30

An element a of a ring R is nilpotent if aⁿ= 0 for some n ∈ Z⁺. Show that the collection of all nilpotent elements in a commutative ring R is an ideal, the nilradical of R.