Serial piecewise domains
A ring \(A\) is called a piecewise domain with respect to the complete set of idempotents \(\{e_1, e_2, \ldots, e_m\}\) if every nonzero homomorphism \(e_iA \rightarrow e_jA\) is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-8682018-03-21T12:35:55Z Serial piecewise domains Gubareni, Nadiya Khibina, Marina piecewise domain, hereditary ring, semihereditary ring, serial ring, Noetherian diagonal, prime radical, prime quiver 16P40, 16G10 A ring \(A\) is called a piecewise domain with respect to the complete set of idempotents \(\{e_1, e_2, \ldots, e_m\}\) if every nonzero homomorphism \(e_iA \rightarrow e_jA\) 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 Algebra and Discrete Mathematics; Vol 6, No 4 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868/398 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2018-03-21T12:35:55Z |
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OJS |
| language |
English |
| topic |
piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 |
| spellingShingle |
piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 Gubareni, Nadiya Khibina, Marina Serial piecewise domains |
| topic_facet |
piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 |
| format |
Article |
| author |
Gubareni, Nadiya Khibina, Marina |
| author_facet |
Gubareni, Nadiya Khibina, Marina |
| author_sort |
Gubareni, Nadiya |
| title |
Serial piecewise domains |
| title_short |
Serial piecewise domains |
| title_full |
Serial piecewise domains |
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Serial piecewise domains |
| title_full_unstemmed |
Serial piecewise domains |
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serial piecewise domains |
| description |
A ring \(A\) is called a piecewise domain with respect to the complete set of idempotents \(\{e_1, e_2, \ldots, e_m\}\) if every nonzero homomorphism \(e_iA \rightarrow e_jA\) 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 |
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AT gubareninadiya serialpiecewisedomains AT khibinamarina serialpiecewisedomains |
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2025-07-17T10:33:02Z |
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2025-07-17T10:33:02Z |
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