N-Products of Relative Flat Modules  

相对平坦模的N-积(英文)

作　　者：赵仁育 刘仲奎 

机构地区：[1]College of Economics and Management, Northwest Normal University [2]Department of Mathematics, Northwest Normal University

出　　处：《Journal of Mathematical Research and Exposition》2008年第4期864-870,共7页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10171082)

摘　　要：Let M be a right R-module and N an infinite cardinal number. A right R-module N is called N-M-coherent if for any 0 ≤ A < B ≤ N, such that B/A → mR for some m ∈ M, if B/A is finitely generated, then B/A is N-fp. A ring R is called N-M-coherent if RR is N-M-coherent. It is proved under some additional conditions that the N-product of any family of M-flat left R-modules is M-flat if and only if R is N-M-coherent. We also give some characterizations of N-M-coherent modules and rings.Let M be a right R-module and N an infinite cardinal number. A right R-module N is called N-M-coherent if for any 0 ≤ A < B ≤ N, such that B/A → mR for some m ∈ M, if B/A is finitely generated, then B/A is N-fp. A ring R is called N-M-coherent if RR is N-M-coherent. It is proved under some additional conditions that the N-product of any family of M-flat left R-modules is M-flat if and only if R is N-M-coherent. We also give some characterizations of N-M-coherent modules and rings.

关 键 词：N-M-coherent module N-M-coherent ring M-flat module. 

分 类 号：O153.3[理学—数学]