Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis On the Rings Whose Injective Modules Are Max-Projective(01. Izmir Institute of Technology, 2023) Yurtsever, Haydar Baran; Büyükaşık, Engin; Büyükaşık, EnginIn this thesis, for some classes of rings including, local, semilocal right semihereditary and right Noetherian right nonsingular, we obtain some conditions that equivalent to being right max-QF. For example, for a semilocal right semihereditary ring, we prove that, the ring is right max-QF if and only if it is a direct product of a semisimple ring and a right small ring. A right Noetherian right nonsingular ring is right max-QF if and only if every injective module can be expressed as a direct sum of an injective module with no maximal submodules and a projective module. We show that, for a ring, being max-QF and almost-QF are not left-right symmetric. An example is given in order to show that max-QF and almost-QF rings are not closed under factor rings.Master Thesis Injective Modules and Their Generalizations(Izmir Institute of Technology, 2018) Demir, Özlem; Büyükaşık, EnginThe main goal of this thesis is to give a survey about some different generalizations of injective modules, namely, C1, C2, C3-conditions and the modules which satisfy the simple versions of these conditions. A right R-module M is called simple-directinjective if every simple submodule which is isomorphic to a direct summand of M is itself a summand, or if the direct sum of any two simple summands whose intersection is zero is a direct summand of M. Firstly, various basic properties and some characterizations of these modules are presented. The relation between simple-direct-injective modules and C3-modules is exhibited. Also, we obtain the structure of simple-direct-injective modules over the ring of integers and over semilocal rings. It is shown that over a commutative ring every nonsingular module is simple-direct-injective.Master Thesis Strongly Noncosingular Modules(Izmir Institute of Technology, 2014) Alagöz, Yusuf; Büyükaşık, EnginThe 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.