2-Lazard-dividable Lie ring
(Redirected from Lie ring whose bracket is the double of a Lie bracket)
Definition
A Lie ring with bracket is termed a 2-Lazard-dividable Lie ring or a Lie ring whose bracket is the double of a Lie bracket if can be equipped with a Lie ring structure with the same additive group and a Lie bracket such that:
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| uniquely 2-divisible Lie ring | ||||
| abelian Lie ring | ||||
| Baer Lie ring | ||||
| Lie ring whose bracket is the double of a Lie bracket giving nilpotency class two |