Master Degree / Yüksek Lisans Tezleri

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

Browse

Filters

2020 - 20232

Settings

Author: search.filters.author.Büyükaşık, EnginPublisher: search.filters.publisher.01. Izmir Institute of Technology

Search Results

Now showing 1 - 2 of 2
  • Master Thesis
    On the Rings Whose Injective Modules Are Max-Projective
    (01. Izmir Institute of Technology, 2023) Büyükaşık, Engin; Büyükaşık, Engin; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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) Büyükaşık, Engin; Büyükaşık, Engin; Durğun, Yılmaz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.