Büyükaşık, EnginGünyüz, Ozan2023-11-132023-11-132010http://standard-demo.gcris.com/handle/123456789/3759Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2010Includes bibliographical references (leaves: 33-34)Text in English; Abstract: Turkish and Englishvii, 34 leavesThis thesis is mainly concerned with the T-noncosingularity issue of a module. Derya Keskin Tutuncu and Rachid Tribak introduced the T-noncosingular modules and gave some properties of these modules. A moduleM is said to be T-noncosingular relative to N if, for every nonzero homomorphism f from M to N, the image of f is not small in N. Inspired by this study, we define a new kind of module, as a particular case of T-noncosingular modules, and call it strongly T-noncosingular modules. We define M to be strongly T-noncosingular relative to N if, for every nonzero homomorphism f from M to N, the image of f is not contained in the radical of N. Obviously, if a module is strongly T-noncosingular, then it is also T-noncosingular, but the converse is, in general, not true. In an attempt to identify the situation when a T-noncosingular module is strongly T-noncosingular, we give necessary and sufficient conditions in terms of the specific ring structures as well as well-known module types.eninfo:eu-repo/semantics/openAccessModules (Algebra)Master Thesis