| Gorenstein平坦维数 |
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| 引用本文： | 李雪妍,张文汇. Gorenstein平坦维数[J]. 吉林大学学报(理学版), 2016, 54(6): 1236 |
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| 作者姓名： | 李雪妍 张文汇 |
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| 作者单位： | 西北师范大学 数学与统计学院, 兰州 730070 |
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| 摘 要： | 设W是包含所有内射模的模类. 通过在任意结合环上引入模的覆盖W-Gorenstein平坦维数, 刻画W-Gorenstein平坦模类的投射可解性, 并证明了: 对任意R 模M和任意正整数n, 若模M的覆盖W-Gorenstein平坦维数为n, 则存在R 模的正合列0→K→H→M→0， 其中[WT]fd(K)=n-1, H是W-Gorenstein平坦模; W- Gorenstein平坦维数不超过覆盖W-Gorenstein平坦维数, 且当覆盖W-Gorenstein平坦维数有限时, 二者相等.
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| 关 键 词： | Gorenstein平坦维数 W-GF闭环 覆盖W-Gorenstein平坦维数 |
| 收稿时间： | 2016-03-01 |
W-Gorenstein Flat Dimension |
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| LI Xueyan,ZHANG Wenhui. W-Gorenstein Flat Dimension[J]. Journal of Jilin University: Sci Ed, 2016, 54(6): 1236 |
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| Authors: | LI Xueyan ZHANG Wenhui |
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| Affiliation: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | Let W be a class of modules that contained all injective modules. By introducing the cover W-Gorenstein flat dimension of modules over associativering, we described that a class of W-Gorenstein flat modules was projectively resolving, and proved that for every R module M and every positiveinteger n, if the cover 〖WTHT〗W〖WT〗 Gorenstein flat dimension of R module M was n, then there existed an exact sequence of R modules 0→K→H→M→0 such that fd(K)=n-1 and H was W-Gorenstein flat module. At the same time, we proved that the W- Gorenstein flat dimension was less than the cover W-Gorenstein flat dimension and they were equivalent when the cover W-Gorenstein flat dimension was finite. |
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| Keywords: | W-Gorenstein flat dimension W-GF closed ring cover W-Gorenstein flat dimension |
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