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 su...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2004 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155957 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639453535731712 |
|---|---|
| author | Shestakov, I. Zhukavets, N. |
| author_facet | Shestakov, I. Zhukavets, N. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-01T01:23:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155957 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T01:23:22Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Shestakov, I. Zhukavets, N. 2019-06-17T15:50:43Z 2019-06-17T15:50:43Z 2004 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. https://nasplib.isofts.kiev.ua/handle/123456789/155957 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On associative algebras satisfying the identity x⁵=0 Article published earlier |
| spellingShingle | On associative algebras satisfying the identity x⁵=0 Shestakov, I. Zhukavets, N. |
| title | 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_short | On associative algebras satisfying the identity x⁵=0 |
| title_sort | on associative algebras satisfying the identity x⁵=0 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155957 |
| work_keys_str_mv | AT shestakovi onassociativealgebrassatisfyingtheidentityx50 AT zhukavetsn onassociativealgebrassatisfyingtheidentityx50 |