The converse to the pure-projective characterization of elementary torsion pairs
Let (T,F)(\mathcal{T},\mathcal{F})(T,F) be an elementary torsion pair in Mod-R\operatorname{Mod}\textrm{-}{R}Mod-R, where RRR is a ring. The torsion class T\mathcal{T}T is said to have enough pure…