TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS  

作　　者：瘳军 郑大彬 刘合国 

机构地区：[1]Faculty of Mathematics and Computer Science,Hubei University

出　　处：《Acta Mathematica Scientia》2010年第5期1769-1775,共7页数学物理学报（B辑英文版）

基　　金：supported in part by NSFC (10371032);Doctoral Foundation of Ministry of Education(20050512002);Youth Foundation of Tianyuan(10726020);Youth Foundation of Hubei Provincial Department of Education(Q20081008)

摘　　要：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.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.

关 键 词：Lie rings derivation towers complete Lie rings 

分 类 号：O152.5[理学—数学]