Essential supplemented modules

In this thesis, the properties of essential supplemented modules, which are a generalization of the essential modules, are examined. For this purpose, the definitions of small submodule, essential submodule, complement submodule, generalized submodule, radical of a module, supplemented modules and generalized supplemented modules, which are the basic concepts we use in our study, are presented and related theorems are given together with their proofs in detail. It has been shown that essential supplemented modules are closed under the finite sums, factor modules and homomorphic images. While M is an essential supplemented module, each finite M-generated R-module has also been shown to be essential supplemented. Necessary and sufficient condition for a ring to be essential supplemented is given. In addition, M has been shown to be essential supplemented if every essential submodule of M is β* equivalent to an essential supplement submodule in M.