On Copurity Of N-cotorsion Modules

In this thesis,we define and study Cn-injective and Cn-flat modules.A left(resp.right)R-module L(resp.M)is said to be Cn-injective(resp.Cn-flat)provided that ExtR1(C.L)= 0(resp.Tor1R(m.C)= 0)for every n-cotorsion left R-module C.We prove that a right R-module M is Cn-flat if and only if M+ is n-injective.Moreover,we use these two classes of modules to characterize some classical rings,that is,a ring R is semisimple Artin if and only if every R-module is Cn-injective,R is von Neumann regular ring if and only if every R-module is Cn-flat module,and R has week global dimension? n if and only if every n-cotortion R-module is Cn-injective.Finally,we study the rings,namely CnI-hereditary rings,which satisfy that every quotient of Cn-injective module is Cn-injective.And we show that CnI-hereditary rings are exactly the rings that every n-cotorsion module has projective dimension? 1.