| 广义P-平坦性和广义P-内射性的一些刻画 |
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| 引用本文： | 王修建,杜先能.广义P-平坦性和广义P-内射性的一些刻画[J].吉林大学学报(理学版),2013,51(4):608-612. |
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| 作者姓名： | 王修建 杜先能 |
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| 作者单位： | 1. 皖西学院 应用数学学院, 安徽 六安 237012; 2. 安徽大学 数学科学学院, 合肥 230600 |
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| 基金项目： | 国家自然科学基金(批准号:11126173) |
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| 摘 要： | 利用同调代数方法分别给出了环R为左GP-内射环、 左GPP-环和左GPF-环的一些等价刻画, 通过引入GP-内射维数和GP-平坦维数的概念, 证明了在左P-凝聚环条件下, 环的左GP-内射整体维数等于环的右GP-弱维数, 并给出了GP-内射维数和GP-平坦维数的若干新刻画.
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| 关 键 词： | GP-平坦模 GP-内射模 GP-平坦维数 GP-内射维数 |
| 收稿时间： | 2012-11-26 |
Some Characterizations on Generalized P Flatness andP-Injectivity |
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| WANG Xiu-jian,DU Xian-neng.Some Characterizations on Generalized P Flatness andP-Injectivity[J].Journal of Jilin University: Sci Ed,2013,51(4):608-612. |
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| Authors: | WANG Xiu-jian DU Xian-neng |
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| Institution: | 1. School of Applied Mathematics, West Anhui University, Lu’an 237012, Anhui Province, China;2. School of Mathematics Sciences, Anhui University, Hefei 230600, China |
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| Abstract: | By means of homological algebra, some equivalent characterizations were given when R was left GP-injective ring, left GPP-ring or left GPF-ring. Having introduced the notions of GP-injective dimensions and GP-flat dimensions, we proved that left GP-injective global dimension is equal to right GP-weak dimension of R under the condition that R is left P-coherent. Furthermore, some new characterizations of GP-injective dimensions and GP-flat dimensions were also given. |
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| Keywords: | GP-flat module GP-injective module GP-flat dimension GP-injective dimension |
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