Idealization of modules

In this thesis, the fundamental informations regarding rings and modules, and definitions, theorems in some distinguished submodules have been given as preliminaries. After these preliminaries, structure of the ring R(+)M which is idealization of a module where R is a commutative ring with identity and M is an R-module has been examined by giving some definitions and properties about the ring, and some new ideals of the ring R(+)M which are homogeneous have been characterized by gathering together informations regarding some specific ideals, were characterized on the ring.