Abstract
Abstract Let R be an IF ring, or be a ring such that each right R-module has a monomorphic flat envelope and the class of flat modules is coresolving. We firstly give a characterization of copure projective and cotorsion modules by lifting and extension diagrams, which implies that the classes of copure projective and cotorsion modules have some balanced properties. Then, a relative right derived functor is introduced to investigate copure projective and cotorsion dimensions of modules. As applications, some new characterizations of QF rings, perfect rings and noetherian rings are given.
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