Almost commutative ring

In algebra, a filtered ring A is said to be almost commutative if the associated graded ring $$\operatorname{gr}A = \oplus A_i/{A_{i-1}}$$ is commutative.

Basic examples of almost commutative rings involve differential operators. For example, the enveloping algebra of a complex Lie algebra is almost commutative by the PBW theorem. Similarly, a Weyl algebra is almost commutative.