Some characterizations of fuzzy small and prime submodules

This work consists of eight sections. In Section 1, we present a literature review and also some definitions and remarks are explained with examples. In Section 2, some basic concepts such as fuzzy set, fuzzy ring, fuzzy module small submodule and prime submodule and several results are presented. In Section 3, the concept of fuzzy small submodules is presented as a generalization of small submodules and investigated some of their properties. In Section 4, some results related to the fuzzy prime submodule and some properties of them are presented. In Section 5, a generalization of small and prime submodules called fuzzy small prime submodules is given. In Section 6, the concept of fuzzy W-prime submodule is studied. In Section 7, the fuzzy S-prime submodule is studied. In Section 8, the important results of this study are discussed