On sum of a nilpotent and an ideally finite algebras
We study associative algebras \(R\) over arbitrary fields which can be decomposed into a sum \(R=A+B\) of their subalgebras \(A\) and \(B\) such that \(A^{2}=0\) and \(B\) is ideally finite (is a sum of its finite dimensional ideals). We prove that \(R\) has a locally nilpotent ideal \(I\) such tha...
Збережено в:
| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/856 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | We study associative algebras \(R\) over arbitrary fields which can be decomposed into a sum \(R=A+B\) of their subalgebras \(A\) and \(B\) such that \(A^{2}=0\) and \(B\) is ideally finite (is a sum of its finite dimensional ideals). We prove that \(R\) has a locally nilpotent ideal \(I\) such that \(R/I\) is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established. |
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