On uniform submodules

In this thesis, the decomposition of the modules into uniform submodules with local endomorphism rings was investigated. In this context, it is aimed to examine the adaptability of Krull-Remak-Schmidt Theorem in different module categories, abel categories and torsion theory. The Krull-Remak-Schmidt Theorem is one of the fundamental and important results, especially in category theory. By adapting this result to different module classes and Torsion theory, results were obtained with the techniques here. In this direction, some concrete examples and applications are given. This thesis consists of five chapters. The first chapter is devoted to the introduction and a general literature is given. In the second part, basic definitions and features related to module concept and torsion theory are given. In the third chapter, the uniform submodules are examined in the module category and in torsion theory. In the fourth section, abel is focused on the uniqueness of uniform separations in categories. In the fifth chapter, the uniqueness of uniform decompositions according to torsion theory is examined.