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...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/832 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
|---|