Quasi-cotilting modules and torsion-free classes

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class CogenM is always a covering class whenever M is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given. As a main result, we prove that there is a bijective correspondence between the equivalent classes of quasi-cotilting modules and torsion-free covering classes.