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Algebra and Discrete Mathematics, 2004, Issue 1, Pages 112–120
(Mi adm331)
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This article is cited in 7 scientific papers (total in 7 papers)
RESEARCH ARTICLE
On associative algebras satisfying the identity $x^5=0$
Ivan P. Shestakova, Natalia Zhukavetsb a Instituto de Matemática e Estatíэstica,
Universidade de São Paulo, Brasil
and Sobolev Institute of Mathematics,
Novosibirsk, Russia
b Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
Abstract:
We study Kuzmin's conjecture on the index of nilpotency for the variety ${\mathcal {N}il}_5$ of associative nil-algebras of degree 5. Due to Vaughan–Lee [11] the problem is reduced to that for $k$-generator ${\mathcal {N}il}_5$-superalgebras, where $k\leq 5$. We confirm Kuzmin's conjecture for 2-generator superalgebras proving that they are nilpotent of degree 15.
Keywords:
Nil-algebra, nilpotency degree, superalgebra.
Received: 22.10.2003 Revised: 27.01.2004
Citation:
Ivan P. Shestakov, Natalia Zhukavets, “On associative algebras satisfying the identity $x^5=0$”, Algebra Discrete Math., 2004, no. 1, 112–120
Linking options:
https://www.mathnet.ru/eng/adm331 https://www.mathnet.ru/eng/adm/y2004/i1/p112
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