数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1769-1775.doi: 10.1016/S0252-9602(10)60170-1

• 论文 • 上一篇    下一篇

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

廖军, 郑大彬, 刘合国   

  1. Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China
  • 收稿日期:2007-03-11 修回日期:2008-12-20 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    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).

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

 LIAO Jun, ZHENG Da-Bin, LIU He-Guo   

  1. Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China
  • Received:2007-03-11 Revised:2008-12-20 Online:2010-09-20 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).

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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.

关键词: Lie rings, derivation towers, complete Lie rings

Abstract:

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

中图分类号: 

  • 17A36
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