| C-投射(内射,平坦)模与优越扩张 |
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| 引用本文： | 陈秀丽,陈建龙.C-投射(内射,平坦)模与优越扩张[J].山东大学学报(理学版),2017,52(8):85-89. |
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| 作者姓名： | 陈秀丽 陈建龙 |
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| 作者单位： | 1. 浙江水利水电学院基础部, 浙江 杭州 310018;2. 东南大学数学系, 江苏 南京 210096 |
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| 基金项目： | 国家自然科学基金资助项目(11371089;61573322) |
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| 摘 要： | 令C作为R-模为半对偶模,其中R为交换环。在(几乎)优越扩张的条件下研究了与半对偶模C相关模类的传递性,讨论了C-投射,内射及平坦预盖及预包的相关性质。作为应用,证明了当环扩张S≥R为优越扩张时,R为诺特环当且仅当S为诺特环;R为凝聚环当且仅当S为凝聚环。
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| 关 键 词： | 优越扩张 平坦)模 凝聚环 半对偶模 C-投射(内射 诺特环 |
| 收稿时间： | 2016-08-22 |
Homological dimensions with respect to semidualizing modules and excellent extensions |
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| CHEN Xiu-li,CHEN Jian-long.Homological dimensions with respect to semidualizing modules and excellent extensions[J].Journal of Shandong University,2017,52(8):85-89. |
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| Authors: | CHEN Xiu-li CHEN Jian-long |
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| Institution: | 1. Department of Basic Courses, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, Zhejiang, China;2. Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China |
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| Abstract: | Let C be a semidualizing R-module with R being a commutative ring. It is investigated the transfer properties of C-homological dimensions under(almost)excellent extensions, and it is discussed that the precovering and preenveloping properties of the C-projectives, C-injectives, and C-flats. As applications, it is proved that if S≥R is an excellent extension, then R is Noetherian if and only if S is Noetherian, and R is coherent if and only if S is coherent. |
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| Keywords: | C-homological dimensions coherent ring Noetherian ring semidualizing module excellent extension |
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