Master Degree / Yüksek Lisans Tezleri

Permanent URI for this collectionhttps://hdl.handle.net/11147/3008

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Author: search.filters.author.Büyükaşık, EnginHas files: Yes

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Now showing 1 - 8 of 8
  • Master Thesis
    On the Rings Whose Injective Modules Are Max-Projective
    (01. Izmir Institute of Technology, 2023) Yurtsever, Haydar Baran; Büyükaşık, Engin; Büyükaşık, Engin
    In 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
    Characterizations of Simple-Direct Modules
    (01. Izmir Institute of Technology, 2020) Diril, Müge; Büyükaşık, Engin; Durğun, Yılmaz
    In this thesis, we study on simple-direct-injective and simple-direct-projective modules. We give a complete characterization of the aforementioned modules simple-direct-injective and simple-direct-projective modules over the ring of integers. The rings whose simple-direct-injective right modules are simple-direct-projective are fully characterized. These are exactly the left perfect right H-rings. The rings whose simple-direct-projective right modules are simple-direct-injective are right max-rings. For a commutative Noetherian ring, we prove that simple-direct-projective modules are simple-direct-injective if and only if simple-direct-injective modules are simple-direct-projective if and only if the ring is Artinian. In addition, Various closure properties and some classes of modules that are simple-direct-injective (resp. projective) are given.
  • Master Thesis
    On Generalization of Hopfian Modules
    (Izmir Institute of Technology, 2018) Yaman, Mehmet; Büyükaşık, Engin
    The notion of Hopfian modules are defined as a generalization of modules of finite length as the modules whose surjective endomorphisms are isomorphisms. These modules and several generalizations of them are extensively studied in the literature. The aim of this thesis is to review some known results and extends some results about generalized Hopfian and weakly Hopfian modules. It is shown that a module is Hopfian if and only if it is both generalized Hopfian and weakly Hopfian. Torsion-free abelian groups are weakly Hopfian. Any nonsingular uniform module is weakly Hopfian. Direct summands of weakly Hopfian modules is weakly Hopfian. It is shown that direct sum weak Hopfian modules is not necessarily weakly Hopfian.
  • Master Thesis
    On the Structure of Modules Characterized by Opposites of Injectivity
    (Izmir Institute of Technology, 2018) Altınay, Ferhat; Büyükaşık, Engin; Büyükaşık, Engin
    In this thesis we consider some problems and also generalize some results related to indigent modules and subinjectivity domains. We prove that subinjectivity domain of any right module is closed under factor modules if and only if the ring is right hereditary. Indigent modules are the modules whose subinjectivity domain is as small as possible, namely the modules whose subinjectivity domain is exactly the class of injective modules. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. The commutative rings whose simple modules are injective or indigent are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We also give a characterization of t.i.b.s. modules over Dedekind domains.
  • Master Thesis
    Injective Modules and Their Generalizations
    (Izmir Institute of Technology, 2018) Demir, Özlem; Büyükaşık, Engin
    The 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, Engin
    The 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.
  • Master Thesis
    Strongly T-Noncosingular Modules
    (Izmir Institute of Technology, 2010) Günyüz, Ozan; Büyükaşık, Engin
    This 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.
  • Master Thesis
    On pseudo semisimple rings
    (Izmir Institute of Technology, 2013) Mutlu, Hatice; Büyükaşık, Engin; Büyükaşık, Engin
    In this thesis, we give a survey of right pseudo semisimple rings and prove some new results about these rings. Namely, we prove that a right pseudo semisimple ring is an internal exchange ring and a right pseudo semisimple ring is an SSP ring. We also give a complete characterization of right and left pseudo semisimple rings.