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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| Дата: | 2012 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152245 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152245 |
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dspace |
| spelling |
irk-123456789-1522452019-06-10T01:25:33Z On radical square zero rings Ringel, C.M. Xiong, B.-L. 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. 2012 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152245 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Ringel, C.M. Xiong, B.-L. |
| spellingShingle |
Ringel, C.M. Xiong, B.-L. On radical square zero rings Algebra and Discrete Mathematics |
| author_facet |
Ringel, C.M. Xiong, B.-L. |
| author_sort |
Ringel, C.M. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152245 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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AT ringelcm onradicalsquarezerorings AT xiongbl onradicalsquarezerorings |
| first_indexed |
2023-05-20T17:37:50Z |
| last_indexed |
2023-05-20T17:37:50Z |
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1796153730217803776 |