Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and on...Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.展开更多
文摘Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.
