Order of an algebraic differential operator
= Order of an algebraic differential operator
{title2=$\operatorname{ord}\theta=\min\{j:\theta\in D_k^j(R)\}$}
The least index in the commutator filtration of the <algebraic differential operator ring> containing a nonzero operator. The zero operator has order $-\infty$ by convention. Equivalently every $(j+1)$-fold iterated commutator with multiplication maps vanishes for an operator of order at most $j$.