Geodesic
On the Nilpotency and Decomposition of Lie-Type Algebras
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 361-372

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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, radical, totally ordered group.
Mots-clés : Lie-type module 
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     author = {N. A. Koreshkov},
     title = {On the {Nilpotency} and {Decomposition} of {Lie-Type} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a3/}
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N. A. Koreshkov. On the Nilpotency and Decomposition of Lie-Type Algebras. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 361-372. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a3/