Lie ring arising as the double of a 3-additive Lazard Lie cring
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
A Lie ring is termed a Lie ring arising as the double of a 3-additive Lazard Lie cring if there exists a 3-additive Lazard Lie cring with cring operation , sharing the same underlying set and additive group as , and such that:
![{\displaystyle [x,y]=2(x*y)\ \forall \ x,y\in L}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e1d53f8e582be1316a7e510c37625232c1df0e3)
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| abelian Lie ring | |FULL LIST, MORE INFO | |||
| Baer Lie ring | |FULL LIST, MORE INFO | |||
| Lie ring whose bracket is the double of a Lie bracket giving nilpotency class two | |FULL LIST, MORE INFO |