On radical square zero rings
Let \(\Lambda\) be a connected left artinian ring with radical square zero and with \(n\) simple modules. If \(\Lambda\) is not self-injective, then we show that any module \(M\) with \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n+1\) is projective. We also determine the structure of t...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7272018-04-04T10:03:23Z On radical square zero rings Ringel, Claus Michael Xiong, Bao-Lin Artin algebras; left artinian rings; representations, modules; Gorenstein modules, CM modules; self-injective algebras; radical square zero algebras 16D90, 16G10; 16G70 Let \(\Lambda\) be a connected left artinian ring with radical square zero and with \(n\) simple modules. If \(\Lambda\) is not self-injective, then we show that any module \(M\) with \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n+1\) is projective. We also determine the structure of the artin algebras with radical square zero and \(n\) simple modules which have a non-projective module \(M\) such that \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727 Algebra and Discrete Mathematics; Vol 14, No 2 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727/259 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T10:03:23Z |
| collection |
OJS |
| language |
English |
| topic |
Artin algebras; left artinian rings; representations modules; Gorenstein modules CM modules; self-injective algebras; radical square zero algebras 16D90 16G10; 16G70 |
| spellingShingle |
Artin algebras; left artinian rings; representations modules; Gorenstein modules CM modules; self-injective algebras; radical square zero algebras 16D90 16G10; 16G70 Ringel, Claus Michael Xiong, Bao-Lin On radical square zero rings |
| topic_facet |
Artin algebras; left artinian rings; representations modules; Gorenstein modules CM modules; self-injective algebras; radical square zero algebras 16D90 16G10; 16G70 |
| format |
Article |
| author |
Ringel, Claus Michael Xiong, Bao-Lin |
| author_facet |
Ringel, Claus Michael Xiong, Bao-Lin |
| author_sort |
Ringel, Claus Michael |
| title |
On radical square zero rings |
| title_short |
On radical square zero rings |
| title_full |
On radical square zero rings |
| title_fullStr |
On radical square zero rings |
| title_full_unstemmed |
On radical square zero rings |
| title_sort |
on radical square zero rings |
| description |
Let \(\Lambda\) be a connected left artinian ring with radical square zero and with \(n\) simple modules. If \(\Lambda\) is not self-injective, then we show that any module \(M\) with \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n+1\) is projective. We also determine the structure of the artin algebras with radical square zero and \(n\) simple modules which have a non-projective module \(M\) such that \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727 |
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AT ringelclausmichael onradicalsquarezerorings AT xiongbaolin onradicalsquarezerorings |
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2025-07-17T10:32:52Z |
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2025-07-17T10:32:52Z |
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1837889878008791040 |