On associative algebras satisfying the identity \(x^5 = 0\)
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...
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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9832018-05-14T08:03:48Z On associative algebras satisfying the identity \(x^5 = 0\) Shestakov, Ivan Zhukavets, Natalia Nil-algebra, nilpotency degree, superalgebra 16R10; 16N40, 16R30, 16W55 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. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983 Algebra and Discrete Mathematics; Vol 3, No 1 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983/512 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-14T08:03:48Z |
| collection |
OJS |
| language |
English |
| topic |
Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 |
| spellingShingle |
Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 Shestakov, Ivan Zhukavets, Natalia On associative algebras satisfying the identity \(x^5 = 0\) |
| topic_facet |
Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 |
| format |
Article |
| author |
Shestakov, Ivan Zhukavets, Natalia |
| author_facet |
Shestakov, Ivan Zhukavets, Natalia |
| author_sort |
Shestakov, Ivan |
| title |
On associative algebras satisfying the identity \(x^5 = 0\) |
| title_short |
On associative algebras satisfying the identity \(x^5 = 0\) |
| title_full |
On associative algebras satisfying the identity \(x^5 = 0\) |
| title_fullStr |
On associative algebras satisfying the identity \(x^5 = 0\) |
| title_full_unstemmed |
On associative algebras satisfying the identity \(x^5 = 0\) |
| title_sort |
on associative algebras satisfying the identity \(x^5 = 0\) |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983 |
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AT shestakovivan onassociativealgebrassatisfyingtheidentityx50 AT zhukavetsnatalia onassociativealgebrassatisfyingtheidentityx50 |
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2025-07-17T10:30:45Z |
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2025-07-17T10:30:45Z |
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1837889836520833024 |