On associative algebras satisfying the identity \(x^5 = 0\)

• Date: 2018
• Main Authors: Shestakov, Ivan, Zhukavets, Natalia
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Nil-algebra; nilpotency degree; superalgebra; 16R10; 16N40; 16R30; 16W55
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983
• Journal Title: Algebra and Discrete Mathematics

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 con...