FT-injective Modules And FT-flat Modules

Let M ∈FPR. If Ext R1(M,E)=0 for any R-module E, then E is called a FT-injective module. If Tor1R(M,E)=0 for any R-module E, then E is called a FT-flat module. In this paper, we study the FT-injective modules and FT-flat modules, and investigate the FT-injective dimension and FT-flat dimension. We show that l.FT-dim(R)=0 if and only if R is FT-semisimple rings if and only if fPD(R)= 0;l.FT-dim(R)≤n if and only if pdRM≤n for any M ∈FPR if and only if fdRM≤n for any M E FPR;l.FT-dim(R)≤1 if and only if R is a FT-hereditary ring.