In this paper ,we introduce a concept of Max– module as follows: M is called a Max- module if ann N R is a maximal ideal of R, for each non– zero submodule N of M;       In other words, M is a Max– module iff (0) is a *- submodule, where  a proper submodule N of M is called a *- submodule if [ ] : N K R is a maximal ideal of R, for each submodule K contains N properly.       In this paper, some properties and characterizations of max– modules and  *- submodules are given. Also, various basic results a bout Max– modules are considered. Moreover, some relations between max- modules and other types of modules are considered.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

The main goal of this paper is to introduce and study a new concept named d^*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d^*-supplement submodule. Many relationships of d^*-supplemented modules are studied. Especially, we give characterizations of d^*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d^*-supplemented and by an example we show that the converse is not true.

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.

Let R be a commutative ring with identity. R is said to be P.P ring if every principle ideal of R is projective. Endo proved that R is P.P ring if and only if Rp is an integral domain for each prime ideal P of R and the total quotient ring Rs of R is regular. Also he proved that R is a semi-hereditary ring if and only if Rp is a valuation domain for each prime ideal P of R and the total quotient Rs of R is regular. , and we study some of properties of these modules. In this paper we study analogue of these results in C.F, C.P, F.G.F, F.G.P R-modules.