Almost commutative ring

{{one source |date=May 2024}}

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