The lifting property refers to a characteristic of certain modules that allows for the extension of morphisms from a submodule to the entire module. Specifically, if a morphism from a submodule can be lifted to a larger module, it indicates that the larger module retains a structure compatible with the operations of the smaller one. This property is especially significant in the context of projective modules, which possess a universal lifting property, meaning every morphism into a projective module can be lifted along any epimorphism.
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