On （m, n）-Coherent Modules and Preenvelopes  

作　　者：SONG Xian-mei1 CHEN Jian-long 

机构地区：[1]Department of Mathematics, Anhui Normal University, Anhui 241000, China [2]Department of Mathematics, Southeast University, Jiangsu 210096, China

出　　处：《Journal of Mathematical Research and Exposition》2008年第1期57-66,共10页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China （No. 10571026）; the Natural Science Foundation of Anhui Provincial Education Department （No. 2006kj050c）; Doctoral Foundation of Anhui Normal University.

摘　　要：In this paper, let m, n be two fixed positive integers and M be a right R-module, we define （m, n）-M-flat modules and （m, n）-coherent modules. A right R-module F is called （m, n）-M-flat if every homomorphism from an （n, m）-presented right R-module into F factors through a module in addM. A left S-module M is called an （m, n）-coherent module if MR is finitely presented, and for any （n, m）-presented right R-module K, Hom（K, M） is a finitely generated left S-module, where S = End（MR）. We mainly characterize （m, n）-coherent modules in terms of preenvelopes （which are monomorphism or epimorphism） of modules. Some properties of （m, n）-coherent rings and coherent rings are obtained as corollaries.In this paper, let m, n be two fixed positive integers and M be a right R-module, we define （m, n）-M-flat modules and （m, n）-coherent modules. A right R-module F is called （m, n）-M-flat if every homomorphism from an （n, m）-presented right R-module into F factors through a module in addM. A left S-module M is called an （m, n）-coherent module if MR is finitely presented, and for any （n, m）-presented right R-module K, Hom（K, M） is a finitely generated left S-module, where S = End（MR）. We mainly characterize （m, n）-coherent modules in terms of preenvelopes （which are monomorphism or epimorphism） of modules. Some properties of （m, n）-coherent rings and coherent rings are obtained as corollaries.

关 键 词：（m  n）-M-flat module （m  n）-coherent module （m  n）-M-flat preenvelope. 

分 类 号：O153.3[理学—数学]