C_n-平坦模的一些结果  

Results on C_n-Flat Modules

作　　者：王茜 王芳贵[2] 沈磊 WANG Xi;WANG Fanggui;SHEN Lei(College of Mathematics,Sichuan University of Arts and Science,Dazhou Sichuan 635000,China;College of Mathematics and Software Science,Sichuan Normal University,Chengdu Sichuan 610066,China)

机构地区：[1]四川文理学院数学学院,四川达州635000 [2]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《广西师范大学学报（自然科学版）》2020年第1期47-53,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11671283);四川文理学院科研启动专项(2019KZ007Z)

摘　　要：本文引入并研究了Cn-平坦模。设R是任何环,n是非负整数,称右R-模M是Cn-平坦模,类指对任何n-余挠左R-模C,都有Tor^R1(M,C)=0。本文证明了M是平坦模当且仅当M是Cn-平坦模且fdRM≤1,Cn-平坦模对纯子模以及其对应的纯商模封闭;还证明了C-平坦模与C1-平坦模就是平坦模,并且当R是整环时,无挠的C2-平坦模也是平坦模;R的弱整体维数不超过n当且仅当任意右R-模的第n次合冲是Cn-平坦模;R是von Neumann正则环当且仅当每个右R-模是Cn-平坦模。Cn-flat module is defined and studied in this paper. A right R-module M is said to be Cn-flat provided that Tor^R1(M, C)=0 for every n-cotorsion left R-module C. It is proved that M is flat if and only if M is Cn-flat and fdRM≤1;and CnF is closed with pure submodules and pure quotient modules. Moreover, C1F and CF are identical to the class of flat modules, in addition, if R is domain and every C2-flat module is also flat module. Finally, R has week global dimension ≤n if and only if the n th-syzygy of any right R-module is Cn-flat, and R is von Neumann regular ring if and only if every right module is Cn-flat module.

关 键 词：n-余挠模 C_n-内射模 C_n-平坦模 弱整体维数 von Neumann正则环 

分 类 号：O154[理学—数学]