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 |
|---|---|
| Date: | 2007 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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| _version_ | 1862723171279437824 |
|---|---|
| author | Gubareni, N. Khibina, M. |
| author_facet | Gubareni, N. Khibina, M. |
| citation_txt | Serial piecewise domains / N. Gubareni, M. Khibina // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 4. — С. 59–72. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-07T18:39:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152382 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:39:47Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Serial piecewise domains Gubareni, N. Khibina, M. |
| title | Serial piecewise domains |
| title_full | Serial piecewise domains |
| title_fullStr | Serial piecewise domains |
| title_full_unstemmed | Serial piecewise domains |
| title_short | Serial piecewise domains |
| title_sort | serial piecewise domains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152382 |
| work_keys_str_mv | AT gubarenin serialpiecewisedomains AT khibinam serialpiecewisedomains |