Acta mathematica scientia, Series B >
TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS
Received date: 2007-03-11
Revised date: 2008-12-20
Online published: 2010-09-20
Supported by
The work is supported in part by NSFC (10371032), Doctoral Foundation of Ministry of Education (20050512002), Youth Foundation of
Tianyuan (10726020) and Youth Foundation of Hubei Provincial Department of Education (Q20081008).
The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.
Key words： Lie rings; derivation towers; complete Lie rings
LIAO Jun , ZHENG Da-Bin , LIU He-Guo . TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1769 -1775 . DOI: 10.1016/S0252-9602(10)60170-1
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