Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Characterizations of Simple-Direct Modules(01. Izmir Institute of Technology, 2020) Diril, Müge; Büyükaşık, Engin; Durğun, YılmazIn 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 The Least Proper Class Containing Weak Supplement(Izmir Institute of Technology, 2009) Durğun, Yılmaz; Alizade, RafailThe main purpose of this thesis is to investigate the least proper class containing the classWS of R-modules determined by weak supplement submodules over a ring R, in particular, over hereditary rings. A submodule A of a module B has(is) weak supplement if and only if there exist a submodule V in B such that A + V . B and the intersection of submodules of A and V is small in B. The classWS does not form a proper class, in general. By extending the class WS, we obtained the least proper class containing the class WS of R-modules over hereditary rings. We investigate the homological objects of the least proper class. We determine the structure of elements of the proper class by submodules.