Master Degree / Yüksek Lisans Tezleri

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

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Subject: search.filters.subject.Simple-direct-injective modules

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  • 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
    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.