Locally nilpotent operator
= Locally nilpotent operator
A linear operator $T$ is locally nilpotent if for each vector $v$ there is an integer $m(v)$ such that $T^{m(v)}v=0$. In finite dimension this is equivalent to being a <nilpotent operator>. Differentiation on the <polynomial ring> is locally nilpotent in characteristic zero but has no uniform nilpotence exponent.