On f - lifting modules

This article introduces the concept for f-lifting modules definition (the R-modules W named f-lifting for T any submodule in W, there is direct summand A for W s.t. A ≤fcoeT in W). Some of the characteristics and examples were given, as well as the relationship between it and the following concepts: lifting module, δ-lifting module, f-hollow module and f-supplemented module.