On the Nilpotency and Decomposition of Lie-Type Algebras

N. A. Koreshkov

Kazan State University

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.

UDC: 512.554

Received: 15.03.2004
Revised: 11.01.2007

DOI: 10.4213/mzm3847

 English version: Mathematical Notes, 2007, 82:3, 321–331

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