Assignment:
Prove that if R is commutative ring and N=(a1,a2,..am) where each ai is a nilpotent element, then N is a nilpotent ideal, i.e N^n=0 for some positive integer n. Deduce that if the nilradical of R is finitely generated then it is a nilpotent ideal.
P.S. the set of nilpotent elements form an ideal which is called nilradical of R for a commutative ring R.
Provide complete and step by step solution for the question and show calculations and use formulas.