Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is called a hollow module if every proper submodule N of M is small (N ≪ M), i.e. N + W ≠ M for every proper submodule W in M. A δ-hollow module is a generalization of hollow module, where an R-module M is called δ-hollow module if every proper submodule N of M is δ-small (N δ  M), i.e. N + W ≠ M for every proper submodule W in M with M W is singular. In this work we study this class of modules and give several fundamental properties related with this concept

  Let R be a commutative ring with unity. In this paper we introduce and study fuzzy distributive modules and fuzzy arithmetical rings as generalizations of (ordinary) distributive modules and arithmetical ring. We give some basic properties about these concepts.  

  In this paper we introduce the notion of semiprime fuzzy module as a generalization of semiprime module. We investigate several characterizations and properties of this concept.

   Let  be a right module over an arbitrary ring  with identity and  . In this work, the coclosed rickart modules as a generalization of  rickart  modules is given. We say  a module  over   coclosed rickart if for each ,   is a coclosed submodule of  . Basic results over this paper are introduced and connections between these modules and otherwise notions are investigated.

  In this paper we introduced the concept of 2-pure submodules as a generalization of pure submodules, we study some of its basic properties and by using this concept we define the class of 2-regular modules, where an R-module M is called 2-regular module if every submodule is 2-pure submodule. Many results about this concept are given. 

There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.