LUCS-Baer 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

A Lie ring L is termed a LUCS-Baer Lie ring if it is a Lie ring of nilpotency class two (i.e., the derived subring is contained in the center) and:

  1. Every element of its derived subring has a unique half in the whole Lie ring.
  2. Every element of its derived subring has a unique half among the elements in the center of the whole Lie ring.
  3. Every element of its derived subring has a unique half among the elements in the Lie ring and that unique half is in the center.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Baer Lie ring 2-powered Lie ring of nilpotency class two |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Lie ring of nilpotency class two |FULL LIST, MORE INFO
LUCS-Lazard Lie ring |FULL LIST, MORE INFO