On radical square zero rings
Let Λ be a connected left artinian ring with radical square zero and with n simple modules. If Λ is not self-injective, then we show that any module M with Exti(M, Λ) = 0 for 1 ≤ i ≤ n + 1 is projective. We also determine the structure of the artin algebras with radical square zero and n simple modu...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152245 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On radical square zero rings / C.M. Ringel, B.-L. Xiong // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 297–306. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862537123991650304 |
|---|---|
| author | Ringel, C.M. Xiong, B.-L. |
| author_facet | Ringel, C.M. Xiong, B.-L. |
| citation_txt | On radical square zero rings / C.M. Ringel, B.-L. Xiong // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 297–306. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let Λ be a connected left artinian ring with radical square zero and with n simple modules. If Λ is not self-injective, then we show that any module M with Exti(M, Λ) = 0 for 1 ≤ i ≤ 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 Exti(M, Λ) = 0 for 1 ≤ i ≤ n.
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| first_indexed | 2025-11-24T11:44:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152245 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T11:44:42Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ringel, C.M. Xiong, B.-L. 2019-06-09T06:14:14Z 2019-06-09T06:14:14Z 2012 On radical square zero rings / C.M. Ringel, B.-L. Xiong // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 297–306. — Бібліогр.: 4 назв. — англ. 1726-3255 2010 MSC:16D90, 16G10; 16G70. https://nasplib.isofts.kiev.ua/handle/123456789/152245 Let Λ be a connected left artinian ring with radical square zero and with n simple modules. If Λ is not self-injective, then we show that any module M with Exti(M, Λ) = 0 for 1 ≤ i ≤ 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 Exti(M, Λ) = 0 for 1 ≤ i ≤ n. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On radical square zero rings Article published earlier |
| spellingShingle | On radical square zero rings Ringel, C.M. Xiong, B.-L. |
| title | 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_short | On radical square zero rings |
| title_sort | on radical square zero rings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152245 |
| work_keys_str_mv | AT ringelcm onradicalsquarezerorings AT xiongbl onradicalsquarezerorings |