New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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    Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,) there exists a submodule X of  such that  f (N)  X ≈ M, where  is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in  embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N.         Moreover, we generalize some properties of weakly N-injectiv

       Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

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.

Let R be an associative ring with identity. An R-module M is called generalized
amply cofinitely supplemented module if every cofinite submodule of M has an
ample generalized supplement in M. In this paper we proved some new results about
this conc- ept.