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 fro...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.展开更多
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.
文摘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.