A decomposition theorem for semiprime rings
A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direc...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9162018-03-21T07:18:38Z A decomposition theorem for semiprime rings Khibina, Marina minor of a ring, local idempotent, semiprime ring, Peirce decomposition 16P40, 16G10 A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direct product of a semisimple Artinian ring and a semiprime \(FDI\)-ring whose identity decomposition doesn't contain artinian idempotents. 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/916 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916/445 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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|
| datestamp_date |
2018-03-21T07:18:38Z |
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OJS |
| language |
English |
| topic |
minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 |
| spellingShingle |
minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 Khibina, Marina A decomposition theorem for semiprime rings |
| topic_facet |
minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 |
| format |
Article |
| author |
Khibina, Marina |
| author_facet |
Khibina, Marina |
| author_sort |
Khibina, Marina |
| title |
A decomposition theorem for semiprime rings |
| title_short |
A decomposition theorem for semiprime rings |
| title_full |
A decomposition theorem for semiprime rings |
| title_fullStr |
A decomposition theorem for semiprime rings |
| title_full_unstemmed |
A decomposition theorem for semiprime rings |
| title_sort |
decomposition theorem for semiprime rings |
| description |
A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direct product of a semisimple Artinian ring and a semiprime \(FDI\)-ring whose identity decomposition doesn't contain artinian idempotents. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916 |
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AT khibinamarina adecompositiontheoremforsemiprimerings AT khibinamarina decompositiontheoremforsemiprimerings |
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2025-07-17T10:34:50Z |
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2025-07-17T10:34:50Z |
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1837890001239539712 |