A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\)
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 t...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1154 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11542018-05-16T05:04:06Z A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) Bekh-Ochir, Chuluun Rankin, Stuart A. 16R10 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 \(W_n\), generated by \(\{x+x^{q^n}, x^{q^n+1}\}\), is maximal, and we proved that \(W_1\) is maximal. In this note, we prove that for \(q=p=3\), \(W_2\) is maximal. Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1154 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1154/647 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
16R10 |
| spellingShingle |
16R10 Bekh-Ochir, Chuluun Rankin, Stuart A. A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| topic_facet |
16R10 |
| format |
Article |
| author |
Bekh-Ochir, Chuluun Rankin, Stuart A. |
| author_facet |
Bekh-Ochir, Chuluun Rankin, Stuart A. |
| author_sort |
Bekh-Ochir, Chuluun |
| title |
A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| title_short |
A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| title_full |
A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| title_fullStr |
A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| title_full_unstemmed |
A maximal \(T\)-space of \(\mathbb{F}_{3}[x]_0\) |
| title_sort |
maximal \(t\)-space of \(\mathbb{f}_{3}[x]_0\) |
| 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 \(W_n\), generated by \(\{x+x^{q^n}, x^{q^n+1}\}\), is maximal, and we proved that \(W_1\) is maximal. In this note, we prove that for \(q=p=3\), \(W_2\) is maximal. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1154 |
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2024-04-12T06:25:08Z |
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2024-04-12T06:25:08Z |
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