On Frobenius full matrix algebras with structure systems
Let \(n\geq 2\) be an integer. In [5] and [6], an \(n\times n\) \(\mathbb{A}\)-full matrix algebra over a field \(K\) is defined to be the set \(\mathbb{M}_n(K)\) of all square \(n\times n\) matrices with coefficients in \(K\) equipped with a multiplication defined by a structure system \(\math...
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| Дата: | 2018 |
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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/832 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-8322018-03-21T11:52:32Z On Frobenius full matrix algebras with structure systems Fujita, Hisaaki Sakai, Yosuke Simson, Daniel Frobenius algebra, quiver, module, socle, tame representation type 16G10, 16G30, 16G60 Let \(n\geq 2\) be an integer. In [5] and [6], an \(n\times n\) \(\mathbb{A}\)-full matrix algebra over a field \(K\) is defined to be the set \(\mathbb{M}_n(K)\) of all square \(n\times n\) matrices with coefficients in \(K\) equipped with a multiplication defined by a structure system \(\mathbb{A}\), that is, an \(n\)-tuple of \(n\times n\) matrices with certain properties. In [5] and [6], mainly \(\mathbb{A}\)-full matrix algebras having \((0,1)\)-structure systems are studied, that is, the structure systems \(\mathbb{A}\) such that all entries are \(0\) or \(1\). In the present paper we study \(\mathbb{A}\)-full matrix algebras having non \((0,1)\)-structure systems. In particular, we study the Frobenius \(\mathbb{A}\)-full matrix algebras. Several infinite families of such algebras with nice properties are constructed in Section 4. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/832 Algebra and Discrete Mathematics; Vol 6, No 1 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/832/363 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Frobenius algebra quiver module socle tame representation type 16G10 16G30 16G60 |
| spellingShingle |
Frobenius algebra quiver module socle tame representation type 16G10 16G30 16G60 Fujita, Hisaaki Sakai, Yosuke Simson, Daniel On Frobenius full matrix algebras with structure systems |
| topic_facet |
Frobenius algebra quiver module socle tame representation type 16G10 16G30 16G60 |
| format |
Article |
| author |
Fujita, Hisaaki Sakai, Yosuke Simson, Daniel |
| author_facet |
Fujita, Hisaaki Sakai, Yosuke Simson, Daniel |
| author_sort |
Fujita, Hisaaki |
| title |
On Frobenius full matrix algebras with structure systems |
| title_short |
On Frobenius full matrix algebras with structure systems |
| title_full |
On Frobenius full matrix algebras with structure systems |
| title_fullStr |
On Frobenius full matrix algebras with structure systems |
| title_full_unstemmed |
On Frobenius full matrix algebras with structure systems |
| title_sort |
on frobenius full matrix algebras with structure systems |
| description |
Let \(n\geq 2\) be an integer. In [5] and [6], an \(n\times n\) \(\mathbb{A}\)-full matrix algebra over a field \(K\) is defined to be the set \(\mathbb{M}_n(K)\) of all square \(n\times n\) matrices with coefficients in \(K\) equipped with a multiplication defined by a structure system \(\mathbb{A}\), that is, an \(n\)-tuple of \(n\times n\) matrices with certain properties. In [5] and [6], mainly \(\mathbb{A}\)-full matrix algebras having \((0,1)\)-structure systems are studied, that is, the structure systems \(\mathbb{A}\) such that all entries are \(0\) or \(1\). In the present paper we study \(\mathbb{A}\)-full matrix algebras having non \((0,1)\)-structure systems. In particular, we study the Frobenius \(\mathbb{A}\)-full matrix algebras. Several infinite families of such algebras with nice properties are constructed in Section 4. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/832 |
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AT fujitahisaaki onfrobeniusfullmatrixalgebraswithstructuresystems AT sakaiyosuke onfrobeniusfullmatrixalgebraswithstructuresystems AT simsondaniel onfrobeniusfullmatrixalgebraswithstructuresystems |
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2024-04-12T06:25:51Z |
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2024-04-12T06:25:51Z |
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