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...
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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/856 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543406436646912 |
|---|---|
| author | Bilun, Svitlana V. |
| author_facet | Bilun, Svitlana V. |
| author_sort | Bilun, Svitlana V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T12:28:31Z |
| description | 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. |
| first_indexed | 2025-12-02T15:43:29Z |
| format | Article |
| id | admjournalluguniveduua-article-856 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:29Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-8562018-03-21T12:28:31Z On sum of a nilpotent and an ideally finite algebras Bilun, Svitlana V. associative algebra, field, sum of subalgebras, finite dimensional ideal, left annihilator 16N40 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. 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/856 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/856/386 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | associative algebra field sum of subalgebras finite dimensional ideal left annihilator 16N40 Bilun, Svitlana V. On sum of a nilpotent and an ideally finite algebras |
| title | On sum of a nilpotent and an ideally finite algebras |
| title_full | On sum of a nilpotent and an ideally finite algebras |
| title_fullStr | On sum of a nilpotent and an ideally finite algebras |
| title_full_unstemmed | On sum of a nilpotent and an ideally finite algebras |
| title_short | On sum of a nilpotent and an ideally finite algebras |
| title_sort | on sum of a nilpotent and an ideally finite algebras |
| topic | associative algebra field sum of subalgebras finite dimensional ideal left annihilator 16N40 |
| topic_facet | associative algebra field sum of subalgebras finite dimensional ideal left annihilator 16N40 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/856 |
| work_keys_str_mv | AT bilunsvitlanav onsumofanilpotentandanideallyfinitealgebras |