Nilpotent Lie ring: Difference between revisions
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A | A [[Lie ring]] is termed a '''nilpotent Lie ring''' if it satisfies the following equivalent conditions: | ||
# Its [[defining ingredient::upper central series of a Lie ring|upper central series]] stabilizes after a finite length at the whole Lie ring. | # Its [[defining ingredient::upper central series of a Lie ring|upper central series]] stabilizes after a finite length at the whole Lie ring. | ||
Latest revision as of 14:12, 13 September 2011
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
Symbol-free definition
A Lie ring is termed a nilpotent Lie ring if it satisfies the following equivalent conditions:
- Its upper central series stabilizes after a finite length at the whole Lie ring.
- Its lower central series stabilizes after a finite length at the zero subring.
- It has a central series.