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.
Asensio MayorJ. and Martínez HernándezJ., Monomorphic flat envelopes in commutative rings, Arch. Math., 54 (1990), 430–435.
Asensio MayorJ. and Martínez HernándezJ., Monomorphic flat envelopes in commutative rings, Arch. Math., 54 (1990), 430–435.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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