A maximal T-space of F₃[x]₀
In earlier work, we have established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]₀, has infinitely many maximal T-spaces, but exactly two maximal T-ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no specific exam...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152343 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A maximal T-space of F₃[x]₀ / C. Bekh-Ochir, S.A. Rankin // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 2. — С. 160–170. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862721448538275840 |
|---|---|
| author | Bekh-Ochir, C. Rankin, S.A. |
| author_facet | Bekh-Ochir, C. Rankin, S.A. |
| citation_txt | A maximal T-space of F₃[x]₀ / C. Bekh-Ochir, S.A. Rankin // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 2. — С. 160–170. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In earlier work, we have established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]₀, has infinitely many maximal T-spaces, but exactly two maximal T-ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no specific examples of maximal T-spaces of k[x]₀ were determined at that time. In a subsequent work, we proposed that for a finite field k of characteristic p > 2 and order q, for each positive integer n which is a power of 2, the T-space Wn, generated by {x + xqⁿ, xqⁿ⁺¹}, is maximal, and we proved that W₁ is maximal. In this note, we prove that for q = p = 3, W₂ is maximal.
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| first_indexed | 2025-12-07T18:30:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152343 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:30:41Z |
| publishDate | 2013 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bekh-Ochir, C. Rankin, S.A. 2019-06-10T10:57:55Z 2019-06-10T10:57:55Z 2013 A maximal T-space of F₃[x]₀ / C. Bekh-Ochir, S.A. Rankin // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 2. — С. 160–170. — Бібліогр.: 5 назв. — англ. 1726-3255 2010 MSC:16R10. https://nasplib.isofts.kiev.ua/handle/123456789/152343 In earlier work, we have established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]₀, has infinitely many maximal T-spaces, but exactly two maximal T-ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no specific examples of maximal T-spaces of k[x]₀ were determined at that time. In a subsequent work, we proposed that for a finite field k of characteristic p > 2 and order q, for each positive integer n which is a power of 2, the T-space Wn, generated by {x + xqⁿ, xqⁿ⁺¹}, is maximal, and we proved that W₁ is maximal. In this note, we prove that for q = p = 3, W₂ is maximal. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A maximal T-space of F₃[x]₀ Article published earlier |
| spellingShingle | A maximal T-space of F₃[x]₀ Bekh-Ochir, C. Rankin, S.A. |
| title | A maximal T-space of F₃[x]₀ |
| title_full | A maximal T-space of F₃[x]₀ |
| title_fullStr | A maximal T-space of F₃[x]₀ |
| title_full_unstemmed | A maximal T-space of F₃[x]₀ |
| title_short | A maximal T-space of F₃[x]₀ |
| title_sort | maximal t-space of f₃[x]₀ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152343 |
| work_keys_str_mv | AT bekhochirc amaximaltspaceoff3x0 AT rankinsa amaximaltspaceoff3x0 AT bekhochirc maximaltspaceoff3x0 AT rankinsa maximaltspaceoff3x0 |