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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2007 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152382 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Serial piecewise domains / N. Gubareni, M. Khibina // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 4. — С. 59–72. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Gubareni, N. Khibina, M. 2019-06-10T17:17:15Z 2019-06-10T17:17:15Z 2007 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 https://nasplib.isofts.kiev.ua/handle/123456789/152382 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Serial piecewise domains Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Serial piecewise domains |
| spellingShingle |
Serial piecewise domains Gubareni, N. Khibina, M. |
| 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 |
| author |
Gubareni, N. Khibina, M. |
| author_facet |
Gubareni, N. Khibina, M. |
| publishDate |
2007 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT gubarenin serialpiecewisedomains AT khibinam serialpiecewisedomains |
| first_indexed |
2025-12-07T18:39:47Z |
| last_indexed |
2025-12-07T18:39:47Z |
| _version_ |
1850875877316886528 |