Homological Characterizations Of Several Representations Of Quivers

In the paper,Strongly matlis flat modules and quasi-Harmanci injective modules are investigated firstly.Let NHI denote the class of quasi-Harmanci injective modules,and SMF denote the class of strongly Matlis flat modules,then(SMF,NHI)is a heredi-tary cotorsion pair.In particular,two hereditary cotorsion pairs(Φ(SMF),Rep(Q,NHI))and(Rep(Q,(SMT),Ψ(NHI))are obtained.Secondly,homological properties of X-Gorenstein projective object,strongly Gorenstein projective object,strongly Gorenstein injective object,strongly Gorenstein flat object and strongly Ding projective object,strongly Ding injective object are characterized in representation category Rep(Q,R).