Referring to the definition given in Exercise 30, find the nilradical of the ring Z₁₂ and observe that it is one of the ideals of Z₁₂ found in Exercise 3. What is the nilradical of Z? of Z₃₂?

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.