Almost commutative ring

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

• Ore condition
• Gelfand–Kirillov dimension

• Victor Ginzburg, Lectures on D-modules

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