Investigation of subprojectivity of cyclic modules

In this thesis, subprojectivity domains of f cyclic modules is investigated. Through the subprojective domains of cyclic modules, new characterizations of well-known algebraic structures such as 𝑃𝑃- ring, 𝐶𝐹-ring and Kasch's ring have been obtained. When M is a cyclic right 𝑅-module and 𝑁 is any singly-projective right 𝑅-module, 𝑀 is an 𝑁-subprojective module. Thus, the subprojectivity domain of a cyclic right R-module includes the class of all singly-projective modules. We have named cyclic modules whose subprojective domain consists precisely of all singly-projective modules as 𝑠𝑖𝑛𝑔𝑝 − 𝑖𝑛𝑑𝑖𝑔𝑒𝑛𝑡. The characterizations of rings over which each non-projective cyclic right 𝑅-module is 𝑠𝑖𝑛𝑔𝑝 − 𝑖𝑛𝑑𝑖𝑔𝑒𝑛𝑡 is investigated. The structure of 𝑠𝑖𝑛𝑔𝑝 − 𝑖𝑛𝑑𝑖𝑔𝑒𝑛𝑡 modules is studied on certain rings. Keywords: Singly-projective module; subprojectivity domain; 𝑠𝑖𝑛𝑔𝑝 − 𝑖𝑛𝑑𝑖𝑔𝑒𝑛𝑡; 𝐶𝐹-ring; 𝑃𝑃- ring