Geodesic
On associative algebras satisfying the identity $x^5=0$
Algebra and discrete mathematics, no. 1 (2004), pp. 112-120.

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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. 
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     title = {On associative algebras satisfying the identity $x^5=0$},
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     number = {1},
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Ivan P. Shestakov; Natalia Zhukavets. On associative algebras satisfying the identity $x^5=0$. Algebra and discrete mathematics, no. 1 (2004), pp. 112-120. http://geodesic.mathdoc.fr/item/ADM_2004_1_a7/