## The Zero is the only Nilpotent Element of the Quotient Ring by its Nilradical

## 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 $\frakN(R/\frakN(R))=0$.

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