Some authors studied modules with annihilator of every nonzero submodule is prime, primary or maximal. In this paper, we introduce and study annsemimaximal and coannsemimaximal modules, where an R-module M is called annsemimaximal (resp. coannsemimaximal) if ann_RN (resp. ) is semimaximal ideal of R for each nonzero submodule N of M.

Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

In this paper we study the concepts of copure submodules and coregular
modules. Many results related with these concepts are obtained.

  Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f Ë› End (M), Imf is pure in M and we give  some properties of this kind of modules.

Let  R be an associative ring with identity and let M be a left R-module . As a generalization of µ-semiregular modules, we introduce an F-µ-semiregular module. Let F be a submodule of M and x∊M. x is called F-µ-semiregular element in M , if there exists a decomposition M=A⨁B, such that A is a projective submodule of  and . M is called  F-µ-semiregular if x is F-µ-semiregular element for each x∊M. A condition under which the module µ-semiregular is F-µ-semiregular module was given. The basic properties and some characterizations of the F-µ-semiregular module were provided.

   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.

  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.

In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.