Serial piecewise domains
A ring A is called a piecewise domain with respect to the complete set of idempotents {e1,e2,…,em} if every nonzero homomorphism eiA→ejA is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary (or semihereditary) rings are equivale...
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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152382 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Serial piecewise domains / N. Gubareni, M. Khibina // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 4. — С. 59–72. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152382 |
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dspace |
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irk-123456789-1523822019-06-11T01:25:28Z Serial piecewise domains Gubareni, N. Khibina, M. A ring A is called a piecewise domain with respect to the complete set of idempotents {e1,e2,…,em} if every nonzero homomorphism eiA→ejA is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary (or semihereditary) rings are equivalent. We prove that a serial right Noetherian ring is a piecewise domain if and only if it is right hereditary. And we prove that a serial ring with right Noetherian diagonal is a piecewise domain if and only if it is semihereditary. 2007 Article Serial piecewise domains / N. Gubareni, M. Khibina // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 4. — С. 59–72. — Бібліогр.: 25 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16P40, 16G10 http://dspace.nbuv.gov.ua/handle/123456789/152382 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 |
A ring A is called a piecewise domain with respect to the complete set of idempotents {e1,e2,…,em} if every nonzero homomorphism eiA→ejA is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary (or semihereditary) rings are equivalent. We prove that a serial right Noetherian ring is a piecewise domain if and only if it is right hereditary. And we prove that a serial ring with right Noetherian diagonal is a piecewise domain if and only if it is semihereditary. |
| format |
Article |
| author |
Gubareni, N. Khibina, M. |
| spellingShingle |
Gubareni, N. Khibina, M. Serial piecewise domains Algebra and Discrete Mathematics |
| author_facet |
Gubareni, N. Khibina, M. |
| author_sort |
Gubareni, N. |
| title |
Serial piecewise domains |
| title_short |
Serial piecewise domains |
| title_full |
Serial piecewise domains |
| title_fullStr |
Serial piecewise domains |
| title_full_unstemmed |
Serial piecewise domains |
| title_sort |
serial piecewise domains |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152382 |
| citation_txt |
Serial piecewise domains / N. Gubareni, M. Khibina // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 4. — С. 59–72. — Бібліогр.: 25 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT gubarenin serialpiecewisedomains AT khibinam serialpiecewisedomains |
| first_indexed |
2023-05-20T17:38:12Z |
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2023-05-20T17:38:12Z |
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1796153743969878016 |