The socle of Leavitt path algebras over a semiprime ring
The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path...
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| Дата: | 2023 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543141894553600 |
|---|---|
| author | Wardati, K. |
| author_facet | Wardati, K. |
| author_sort | Wardati, K. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-02-08T16:55:57Z |
| description | The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points. |
| first_indexed | 2026-02-08T07:58:31Z |
| format | Article |
| id | admjournalluguniveduua-article-1850 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:31Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-18502023-02-08T16:55:57Z The socle of Leavitt path algebras over a semiprime ring Wardati, K. reduction theorem, semiprime, socle, line point Primary 16S88; Secondary 16D70 The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points. Lugansk National Taras Shevchenko University LPPM UIN Sunan Kalijaga, Cluster of Research Leader, 2019 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850 10.12958/adm1850 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| spellingShingle | reduction theorem semiprime socle line point Primary 16S88 Secondary 16D70 Wardati, K. The socle of Leavitt path algebras over a semiprime ring |
| title | The socle of Leavitt path algebras over a semiprime ring |
| title_full | The socle of Leavitt path algebras over a semiprime ring |
| title_fullStr | The socle of Leavitt path algebras over a semiprime ring |
| title_full_unstemmed | The socle of Leavitt path algebras over a semiprime ring |
| title_short | The socle of Leavitt path algebras over a semiprime ring |
| title_sort | socle of leavitt path algebras over a semiprime ring |
| topic | reduction theorem semiprime socle line point Primary 16S88 Secondary 16D70 |
| topic_facet | reduction theorem semiprime socle line point Primary 16S88 Secondary 16D70 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850 |
| work_keys_str_mv | AT wardatik thesocleofleavittpathalgebrasoverasemiprimering AT wardatik socleofleavittpathalgebrasoverasemiprimering |