(m,n)-phantom Morphism And (m,n)-Ext-phantom Morphism

In the thesis,we introduce the concepts of(m,n)-phantom morphism and(m,n)-Ext-phantom morphism based on finitely m-presented modules.We provide some homological properties of(m,n)-phantom and(m,n)-Ext-phantom morphism-s,and investigate the existences of(m,n)-phantom((m,n)-Ext-phantom)precover and preenvelope.As an application,we characterize the weak global dimension of a right n-coherent ring in terms of(m,n)-Ext-phantom cover.In addition,we intro-duce(m,n)-Tor-epimorphism and(m,n)-Ext-monomorphism,and discuss the rela-tionship between(m,n)-phantom morphism(resp.(m,n)-Ext-phantom morphism)and(m,n)-Tor-epimorphism(resp.(m,n)-Ext-monomorphism)...