On associative algebras satisfying the identity x⁵=0
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...
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| Дата: | 2004 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155957 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On associative algebras satisfying the identity x⁵=0 / I. Shestakov, N. Zhukavets // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 112–120. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-155957 |
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dspace |
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irk-123456789-1559572019-06-18T01:30:48Z On associative algebras satisfying the identity x⁵=0 Shestakov, I. Zhukavets, N. 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. 2004 Article On associative algebras satisfying the identity x⁵=0 / I. Shestakov, N. Zhukavets // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 112–120. — Бібліогр.: 13 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16R10; 16N40, 16R30, 16W55. http://dspace.nbuv.gov.ua/handle/123456789/155957 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Shestakov, I. Zhukavets, N. |
| spellingShingle |
Shestakov, I. Zhukavets, N. On associative algebras satisfying the identity x⁵=0 Algebra and Discrete Mathematics |
| author_facet |
Shestakov, I. Zhukavets, N. |
| author_sort |
Shestakov, I. |
| title |
On associative algebras satisfying the identity x⁵=0 |
| title_short |
On associative algebras satisfying the identity x⁵=0 |
| title_full |
On associative algebras satisfying the identity x⁵=0 |
| title_fullStr |
On associative algebras satisfying the identity x⁵=0 |
| title_full_unstemmed |
On associative algebras satisfying the identity x⁵=0 |
| title_sort |
on associative algebras satisfying the identity x⁵=0 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155957 |
| citation_txt |
On associative algebras satisfying the identity x⁵=0 / I. Shestakov, N. Zhukavets // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 112–120. — Бібліогр.: 13 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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AT shestakovi onassociativealgebrassatisfyingtheidentityx50 AT zhukavetsn onassociativealgebrassatisfyingtheidentityx50 |
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2023-05-20T17:48:36Z |
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2023-05-20T17:48:36Z |
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1796154138277445632 |