Air-gap flash

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

See also

• Ore condition
• Gelfand–Kirillov dimension

References

• Victor Ginzburg, Lectures on D-modules

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