Author(s): SONG Xian-mei, CHEN Jian-long
Pages: 57-66
Year: 2008 Issue:  1
Journal: JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
Keyword:  (m; n)-M-flat module; (m; n)-coherent module; (m; n)-M-flat preenvelope;
Abstract: 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,Horn(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.