## Problem 725

Prove that if $R$ is a commutative ring and $\frakN(R)$ is its nilradical, then the zero is the only nilpotent element of $R/\frakN(R)$. That is, show that $\frakN(R/\frakN(R))=0$.

## Problem 620

Is it true that a set of nilpotent elements in a ring $R$ is an ideal of $R$?

If so, prove it. Otherwise give a counterexample.