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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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Інститут прикладної математики і механіки НАН України
2013
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/152343 |
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irk-123456789-1523432019-06-11T01:25:03Z A maximal T-space of F₃[x]₀ Bekh-Ochir, C. Rankin, S.A. 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. 2013 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152343 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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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. |
| format |
Article |
| author |
Bekh-Ochir, C. Rankin, S.A. |
| spellingShingle |
Bekh-Ochir, C. Rankin, S.A. A maximal T-space of F₃[x]₀ Algebra and Discrete Mathematics |
| author_facet |
Bekh-Ochir, C. Rankin, S.A. |
| author_sort |
Bekh-Ochir, C. |
| title |
A maximal T-space of F₃[x]₀ |
| title_short |
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_sort |
maximal t-space of f₃[x]₀ |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152343 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bekhochirc amaximaltspaceoff3x0 AT rankinsa amaximaltspaceoff3x0 AT bekhochirc maximaltspaceoff3x0 AT rankinsa maximaltspaceoff3x0 |
| first_indexed |
2023-05-20T17:38:06Z |
| last_indexed |
2023-05-20T17:38:06Z |
| _version_ |
1796153739216683008 |