Rings which have \((m, n)\)-flat injective modules
A ring \(R\) is said to be a left \(IF-(m,n)\) ring if every injective left \(R\)-module is \((m,n)\)-flat. In this paper, several characterizations of left \(IF-(m,n)\) rings are investigated, some conditions under which \(R\) is left \(IF-(m,n)\) are given. Furthermore, conditions under w...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/947 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9472018-03-21T06:49:56Z Rings which have \((m, n)\)-flat injective modules Zhanmin, Zhu Zhangsheng, Xia injective modules; (m, n)-flat modules; left IF−(m, n) rings; left IF − 1 rings 16D50, 16E65 A ring \(R\) is said to be a left \(IF-(m,n)\) ring if every injective left \(R\)-module is \((m,n)\)-flat. In this paper, several characterizations of left \(IF-(m,n)\) rings are investigated, some conditions under which \(R\) is left \(IF-(m,n)\) are given. Furthermore, conditions under which a left \(IF-1\) ring (i.e., \(IF-(1,1)\) ring) is a field, a regular ring and a semisimple ring are studied respectively. 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/947 Algebra and Discrete Mathematics; Vol 4, No 4 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/947/476 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
injective modules; (m n)-flat modules; left IF−(m n) rings; left IF − 1 rings 16D50 16E65 |
| spellingShingle |
injective modules; (m n)-flat modules; left IF−(m n) rings; left IF − 1 rings 16D50 16E65 Zhanmin, Zhu Zhangsheng, Xia Rings which have \((m, n)\)-flat injective modules |
| topic_facet |
injective modules; (m n)-flat modules; left IF−(m n) rings; left IF − 1 rings 16D50 16E65 |
| format |
Article |
| author |
Zhanmin, Zhu Zhangsheng, Xia |
| author_facet |
Zhanmin, Zhu Zhangsheng, Xia |
| author_sort |
Zhanmin, Zhu |
| title |
Rings which have \((m, n)\)-flat injective modules |
| title_short |
Rings which have \((m, n)\)-flat injective modules |
| title_full |
Rings which have \((m, n)\)-flat injective modules |
| title_fullStr |
Rings which have \((m, n)\)-flat injective modules |
| title_full_unstemmed |
Rings which have \((m, n)\)-flat injective modules |
| title_sort |
rings which have \((m, n)\)-flat injective modules |
| description |
A ring \(R\) is said to be a left \(IF-(m,n)\) ring if every injective left \(R\)-module is \((m,n)\)-flat. In this paper, several characterizations of left \(IF-(m,n)\) rings are investigated, some conditions under which \(R\) is left \(IF-(m,n)\) are given. Furthermore, conditions under which a left \(IF-1\) ring (i.e., \(IF-(1,1)\) ring) is a field, a regular ring and a semisimple ring are studied respectively. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/947 |
| work_keys_str_mv |
AT zhanminzhu ringswhichhavemnflatinjectivemodules AT zhangshengxia ringswhichhavemnflatinjectivemodules |
| first_indexed |
2024-04-12T06:25:30Z |
| last_indexed |
2024-04-12T06:25:30Z |
| _version_ |
1796109224812478464 |