In our previous work, we submitted a concept about small-singular submodules. In this paper, we create a new concept, namely ƒ-small submodules, this concept is an extension of small submodules. A submodule H of an R-module M is named ƒ-small if H+K=M and M/K is small-singular, then K=M. Some characteristics are given in addition to their relationship to some of the concepts and the equivalence between them is studied. Additionally, we introduce a generalization of supplemented module namely ƒ-supplemented modules as well, we illustrate its relation with δ– supplemented modules

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