Metabelian Lie ring

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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 L is termed metabelian if ...
1 its derived subring is abelian its derived subring [L,L] is an abelian Lie ring
2 it has an abelian ideal with abelian quotient ring there is an abelian ideal I of L such that the quotient ring L/I is abelian
3 its second derived subring is zero [[L,L],[L,L]] = 0. In other words, [[a,b],[c,d]] = 0 for all a,b,c,d \in L