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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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543328191905793 |
|---|---|
| author | Shestakov, Ivan Zhukavets, Natalia |
| author_facet | Shestakov, Ivan Zhukavets, Natalia |
| author_sort | Shestakov, Ivan |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-14T08:03:48Z |
| 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. |
| first_indexed | 2025-12-02T15:29:00Z |
| format | Article |
| id | admjournalluguniveduua-article-983 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:29:00Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 Shestakov, Ivan Zhukavets, Natalia On associative algebras satisfying the identity \(x^5 = 0\) |
| title | 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_short | On associative algebras satisfying the identity \(x^5 = 0\) |
| title_sort | on associative algebras satisfying the identity \(x^5 = 0\) |
| topic | Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 |
| topic_facet | Nil-algebra nilpotency degree superalgebra 16R10; 16N40 16R30 16W55 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/983 |
| work_keys_str_mv | AT shestakovivan onassociativealgebrassatisfyingtheidentityx50 AT zhukavetsnatalia onassociativealgebrassatisfyingtheidentityx50 |