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| | In algebra, a [[filtered ring]] ''A'' is said to be '''almost commutative''' if the associated graded ring <math>\operatorname{gr}A = \oplus A_i/{A_{i-1}}</math> is [[commutative ring|commutative]]. |
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| | 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. |
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| | == See also == |
| | *[[Ore condition]] |
| | *[[Gelfand–Kirillov dimension]] |
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| | == References == |
| | *[[Victor Ginzburg]], [http://www.math.harvard.edu/~gaitsgde/grad_2009/Ginzburg.pdf Lectures on D-modules] |
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| | {{algebra-stub}} |
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| | [[Category:Ring theory]] |
Revision as of 12:02, 11 August 2013
In algebra, a filtered ring A is said to be almost commutative if the associated graded ring 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
References
Template:Algebra-stub