Graded derivation
= Graded derivation
{title2=$Q(ab)=(Qa)b+(-1)^{|a|}a(Qb)$}
An odd graded derivation satisfies $Q(ab)=(Qa)b+(-1)^{|a|}a(Qb)$ for homogeneous $a$. Its square is an even derivation; consequently checking $Q^2=0$ on algebra generators establishes nilpotence everywhere.