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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | 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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Algebra and Discrete Mathematics| _version_ | 1856543044455628800 |
|---|---|
| author | Khibina, Marina |
| author_facet | Khibina, Marina |
| author_sort | Khibina, Marina |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:18:38Z |
| 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. |
| first_indexed | 2025-12-02T15:41:25Z |
| format | Article |
| id | admjournalluguniveduua-article-916 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:25Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 Khibina, Marina A decomposition theorem for semiprime rings |
| title | 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_short | A decomposition theorem for semiprime rings |
| title_sort | decomposition theorem for semiprime rings |
| topic | minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 |
| topic_facet | minor of a ring local idempotent semiprime ring Peirce decomposition 16P40 16G10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916 |
| work_keys_str_mv | AT khibinamarina adecompositiontheoremforsemiprimerings AT khibinamarina decompositiontheoremforsemiprimerings |