| 交换环上的w-P-平坦模及其应用 |
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| 引用本文： | 夏伟恒,乔磊,宋菲菲.交换环上的w-P-平坦模及其应用[J].吉林大学学报(理学版),2022,60(2):269-276. |
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| 作者姓名： | 夏伟恒 乔磊 宋菲菲 |
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| 作者单位： | 四川师范大学 数学科学学院, 成都 610066 |
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| 摘 要： | 利用交换环上的w-模理论对P-平坦模进行w-模化研究. 首先引入交换环上w-P-平坦模的概念, 并讨论w-P-平坦模的一些刻画和性质； 其次作为应用, 给出von Neumann正则环和p.p环(即每个主理想是投射理想的环)的一些新刻画.
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| 关 键 词： | w-P-平坦模 p.p环 w-p.f环 |
| 收稿时间： | 2021-07-13 |
w-P-Flat Modules over Commutative Rings and Their Applications |
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| XIA Weiheng,QIAO Lei,SONG Feifei.w-P-Flat Modules over Commutative Rings and Their Applications[J].Journal of Jilin University: Sci Ed,2022,60(2):269-276. |
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| Authors: | XIA Weiheng QIAO Lei SONG Feifei |
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| Institution: | School of Mathematical Science, Sichuan Normal University, Chengdu 610066, China |
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| Abstract: | We studied the w-module theoretic analogue of P-flat modules by using w-module theory over commutative rings. Firstly, we introduced the concept of w-P-flat modules over commutative rings and discussed several characterizations and properties of w-P-flat modules. Secondly, as applications of w-P-lat modules, we give some new characterizations of von Neumann regular rings and p.p rings (i.e., rings in which every principle ideal is a projective ideal). |
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| Keywords: | w-P-flat module p p ring w-p f ring |
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