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Small non-associative division algebras up to isotopy
We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras...
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Інститут прикладної математики і механіки НАН України
2010
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/154498 |
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irk-123456789-1544982019-06-16T01:32:25Z Small non-associative division algebras up to isotopy Schwarz, T. We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras of size 4, 8, and 9 are isotopes of a Galois field, whereas there are three isotopy classes of division algebras with 16 elements. 2010 Article Small non-associative division algebras up to isotopy / T. Schwarz // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 103–108. — Бібліогр.: 4 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:17D99. http://dspace.nbuv.gov.ua/handle/123456789/154498 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
| description |
We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras of size 4, 8, and 9 are isotopes of a Galois field, whereas there are three isotopy classes of division algebras with 16 elements. |
| format |
Article |
| author |
Schwarz, T. |
| spellingShingle |
Schwarz, T. Small non-associative division algebras up to isotopy Algebra and Discrete Mathematics |
| author_facet |
Schwarz, T. |
| author_sort |
Schwarz, T. |
| title |
Small non-associative division algebras up to isotopy |
| title_short |
Small non-associative division algebras up to isotopy |
| title_full |
Small non-associative division algebras up to isotopy |
| title_fullStr |
Small non-associative division algebras up to isotopy |
| title_full_unstemmed |
Small non-associative division algebras up to isotopy |
| title_sort |
small non-associative division algebras up to isotopy |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154498 |
| citation_txt |
Small non-associative division algebras up to isotopy / T. Schwarz // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 103–108. — Бібліогр.: 4 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT schwarzt smallnonassociativedivisionalgebrasuptoisotopy |
| first_indexed |
2023-05-20T17:44:52Z |
| last_indexed |
2023-05-20T17:44:52Z |
| _version_ |
1796153996045451264 |