Subprojectivity profile of goldie torsion modules

This thesis focuses on the study of subprojective domains of Goldie torsion modules. This study aims to extend the theoretical foundations of subprojectivity domains of Goldie torsion modules. We studied them as a structure with wider applications and to reveal their role in the classification of rings. The aim of our thesis is first to study the categorical properties of subprojectivity domians of Goldie torsion modules. Second, we will investigate the subprojectivity profile (sp-profile) of Goldie torsion modules on a ring R, studying some of its properties and considering how these properties determine ring structures. Additionally, we study Goldie torsion in terms of the lattice theory of this profile. Our thesis consists of four main sections. The first section provides information about the historical development and motivation of the topic under consideration. The second section provides some necessary basic information and the homological properties of some special rings to facilitate understanding of the other sections. The third section deals with the subprojective domains of modules. The final section characterizes some rings using the properties of the subprojectivity profile of Goldie torsion modules. Keywords: Goldie torsion module, Goldie torsion subprojectivity domains, Goldie torsion subprojectivity profile, nonsingular ring