Multiplication modules over noncommutative ring

The main subject of this thesis is to define the characteristics and properties of module theory and multiplication modules in module theory over noncommuative rings. First of all,in section 2 is given the required information for being able to remind the basic concepts. So that, the sub-structure was established to introduce to the Ring Theory and Module Theory. In section 3, the general structure and the condition of being commutative and noncommutative of the rings are described. In the next section, definition and basic properties of the modules are given. Thus, all knowledge and properties of the modules are presented to examine the construction of the multiplication modules. In section 5, firstly, general characteristics and definitions of the multiplication modules over the noncommutative ring are given. Some examples are presented to support this definition and properties. Then, the special situation of the multiplication modules such as, essantial, uniform, prime, distributive modules are investigated. Nextly, the finitely generated multiplication modules and the structure of the maximal submodules of the multiplication modules are dealt. Finally, the behaviours of the multiplication modules over the noncommutative ring with commutative multiplication of ideals are investigated and showed.