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Matematicheskie Zametki, 2007, Volume 82, Issue 3, Pages 361–372
DOI: https://doi.org/10.4213/mzm3847 (Mi mzm3847) 		 
On the Nilpotency and Decomposition of Lie-Type Algebras

N. A. Koreshkov

Kazan State University
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DOI: https://doi.org/10.4213/mzm3847
Abstract: In the paper, an analog of the Engel theorem for graded algebras admitting a Lie-type module is proved. Moreover, it is shown that every semisimple algebra of associative type with ordered grading and one-dimensional grading subspaces is the direct sum of two-sided ideals that are simple algebras.
Keywords: algebra of associative type, semisimple algebra, graded algebra, Engel theorem, Lie-type module, radical, totally ordered group.
Received: 15.03.2004
Revised: 11.01.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 3, Pages 321–331
DOI: https://doi.org/10.1134/S0001434607090040
Bibliographic databases:
UDC: 512.554
Language: Russian
Citation: N. A. Koreshkov, “On the Nilpotency and Decomposition of Lie-Type Algebras”, Mat. Zametki, 82:3 (2007), 361–372; Math. Notes, 82:3 (2007), 321–331
Citation in format AMSBIB
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