Solution
= Solution
If $a^m=b^n=0$, then every term in $(a+b)^{m+n-1}$ vanishes; also $(ra)^m=0$. Thus the nilpotents form an <ideal> $N$. The quotient $R/N$ has no nonzero nilpotents.
= Solution
If $a^m=b^n=0$, then every term in $(a+b)^{m+n-1}$ vanishes; also $(ra)^m=0$. Thus the nilpotents form an <ideal> $N$. The quotient $R/N$ has no nonzero nilpotents.