On associative algebras satisfying the identity x⁵=0 - Shestakov, I.; Zhukavets, N. (Algebra and Discrete Mathematics, 2004)
We study Kuzmin’s conjecture on the index of
nilpotency for the variety N il₅ of associative nil-algebras of degree 5. Due to Vaughan-Lee [11] the problem is reduced to that
for k-generator N il₅-superalgebras, where k ≤ 5. We confirm
Kuzmin’s conjecture for 2-generator superalgebras proving that
they are nilpotent of degree 15.