Metabelian Lie ring
This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
View a complete list of properties of Lie rings
VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions
Definition
| No. | A Lie ring is termed metabelian if ... | A Lie ring is termed metabelian if ... |
|---|---|---|
| 1 | its derived subring is abelian | its derived subring is an abelian Lie ring |
| 2 | it has an abelian ideal with abelian quotient ring | there is an abelian ideal of such that the quotient ring is abelian |
| 3 | its second derived subring is zero | . In other words, for all |
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![{\displaystyle [[L,L],[L,L]]=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ddd862114aa0eb7a7edd8b2817763b55e346af5)
![{\displaystyle [[a,b],[c,d]]=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79e36c9cb15cd844aed9cee6aa0517bdeda2a23f)
