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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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 \(1 \le i \le n\). |
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