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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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2013
Hauptverfasser: Bekh-Ochir, C., Rankin, S.A.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2013
Online Zugang: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
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-152343
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A maximal T-space of F₃[x]₀
spellingShingle A maximal T-space of F₃[x]₀
Bekh-Ochir, C.
Rankin, S.A.
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
author Bekh-Ochir, C.
Rankin, S.A.
author_facet Bekh-Ochir, C.
Rankin, S.A.
publishDate 2013
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
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.
issn 1726-3255
url https://nasplib.isofts.kiev.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.
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first_indexed 2025-12-07T18:30:41Z
last_indexed 2025-12-07T18:30:41Z
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