Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k....Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.展开更多
Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes th...Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes the class of all f-projective （f-injective） right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.展开更多
Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
文摘Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.
基金the Jiangsu Teachers University of Technology of China(No.Kyy06109)
文摘Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes the class of all f-projective （f-injective） right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.
基金National Natural Science Foundation of China(10171082)by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE.
文摘Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
