Büyükaşık, EnginAlagöz, Yusuf2023-11-132023-11-132014http://standard-demo.gcris.com/handle/123456789/3946Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2014Includes bibliographical references (leaves: 38-39)Text in English; Abstract: Turkish and Englishvii, 39 leavesThe main purpose of this thesis is to investigate the notion of strongly noncosingular modules. We call a right R-module M strongly noncosingular if for every nonzero right R module N and every nonzero homomorphismf : M → N, Im(f) is not a cosingular (or Radsmall) submodule of N in the sense of Harada. It is proven that (1) A right R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective right R-modules coincides with the class of (strongly) noncosingular right R-modules; (3) a right hereditary ring R is Max-ring if and only if absolutely coneat right R-modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective R-modules coincides with the class of strongly noncosingular R-modules.eninfo:eu-repo/semantics/openAccessR-modulesModules (Algebra)RingsMaster Thesis