LUCS-Baer Lie ring: Difference between revisions
(Created page with "{{wikilocal}} {{Lie ring property}} ==Definition== A Lie ring <math>L</math> is termed a '''LUCS-Baer Lie ring''' if it is a Lie ring of nilpotency class two (i.e., ...") |
|||
| Line 26: | Line 26: | ||
|- | |- | ||
| [[Stronger than::Lie ring of nilpotency class two]] || || || || {{intermediate notions short|Lie ring of nilpotency class two|LUCS-Baer Lie ring}} | | [[Stronger than::Lie ring of nilpotency class two]] || || || || {{intermediate notions short|Lie ring of nilpotency class two|LUCS-Baer Lie ring}} | ||
|- | |||
| [[Stronger than::LUCS-Lazard Lie ring]] || || || || {{intermediate notions short|LUCS-Lazard Lie ring|LUCS-Baer Lie ring}} | |||
|} | |} | ||
Latest revision as of 19:29, 5 August 2013
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 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:
- Every element of its derived subring has a unique half in the whole Lie ring.
- Every element of its derived subring has a unique half among the elements in the center of the whole Lie ring.
- 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 |