On τ-coherent rings

We study left-right symmetry of rings for which every fnitely generated torsion free left (or right) module is embedded into free modules. We give a necessary and sufficient condition of a ring R with flat left injective hulls under which R has a flat right injective hull. Let Q be a left coherent maximal left quotient ring of R such that every finitely presented left Q-module is torsion free. Then, Q_R is flat if and only if R is left τ-coherent, relative to Lambek torsion theory.