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, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

Let R be commutative ring with identity and let M be any unitary left R-module. In this paper we study the properties of ec-closed submodules, ECS- modules and the relation between ECS-modules and other kinds of modules. Also, we study the direct sum of ECS-modules.

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.

Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.

Let
be an
module,
be a fuzzy soft module over
, and
be a fuzzy soft ring over
, then
is called FSFS module if and only if
is an
module. In this paper, we introduce the concept of
Noetherian and
Artinian modules and finally we investigate some basic properties of
Noetherian and
Artinian modules.

In this paper, we introduce the concept of e-small Projective modules as a generlization of Projective modules.

    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.